Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1416 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×#1113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×#1113 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×SD16×C3⋊D3 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #11723708 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11723704 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11723646 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C8×#1113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D32×SD16 | — | 3 | 3 | no | maximal |
| 9 | C22×#1113 | — | 2 | 1 | no | — |
| 10 | C3×Q8×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 11 | C3×D4×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 12 | #89049 | — | 2 | 3 | no | — |
| 13 | C4⋊#1113 | C22 | 1 | 3 | yes | — |
| 14 | C4×#1113 | — | 2 | 1 | no | — |
| 15 | C4×#1113 | C22 | 1 | 1 | yes | characteristic |
| 16 | #89040 | — | 2 | 3 | no | — |
| 17 | #89040 | C22 | 1 | 3 | yes | complemented |
| 18 | C33×SD16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#3755 | C22 | 1 | 3 | yes | complemented |
| 20 | C3×#3754 | C22 | 1 | 3 | yes | complemented |
| 21 | C3×#3744 | C22 | 1 | 3 | yes | complemented |
| 22 | C3×C8×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 23 | #88811 | C22 | 1 | 6 | yes | complemented |
| 24 | #88808 | C22 | 1 | 3 | yes | complemented |
| 25 | D32×Q8 | — | 3 | 3 | no | — |
| 26 | D32×D4 | — | 3 | 3 | no | — |
| 27 | SD16×C3⋊D3 | D3 | 1 | 3 | yes | complemented |
| 28 | C3×D3×SD16 | — | 3 | 6 | no | — |
| 29 | C3×D3×SD16 | — | 6 | 3 | no | — |
| 30 | #63940 | — | 3 | 3 | no | — |
| 31 | D3×#215 | — | 3 | 6 | no | — |
| 32 | #63930 | — | 3 | 3 | no | — |
| 33 | D3×#214 | — | 3 | 6 | no | — |
| 34 | #63796 | — | 3 | 3 | no | — |
| 35 | D3×#204 | — | 3 | 6 | no | — |
| 36 | D32×C8 | — | 3 | 3 | no | — |
| 37 | C22×C3×C3⋊D3 | — | 2 | 3 | no | — |
| 38 | C2×#1113 | — | 2 | 3 | no | — |
| 39 | C2×#1113 | — | 4 | 4 | no | — |
| 40 | C2×#1113 | D4 | 1 | 1 | yes | characteristic |
| 41 | C33×Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 42 | C33×D4 | C23 | 1 | 1 | yes | characteristic |
| 43 | C3×#638 | — | 2 | 3 | no | — |
| 44 | C3×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 45 | C3×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 46 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 47 | C3×#634 | — | 2 | 3 | no | — |
| 48 | C3×#634 | C23 | 1 | 3 | yes | complemented |
| 49 | #6296 | — | 2 | 3 | no | — |
| 50 | #6295 | — | 2 | 3 | no | — |
| 51 | #6294 | — | 2 | 3 | no | — |
| 52 | #6294 | D4 | 1 | 3 | yes | — |
| 53 | C33×C8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 54 | C3×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | complemented |
| 55 | C2×D3×SD16 | — | 9 | 3 | no | — |
| 56 | C22×D32 | — | 6 | 3 | no | — |
| 57 | Q8×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 58 | D4×C3⋊D3 | C2×D3 | 1 | 3 | yes | — |
| 59 | C3×D3×Q8 | — | 3 | 6 | no | — |
| 60 | C3×D3×Q8 | — | 6 | 3 | no | — |
| 61 | C3×D3×D4 | — | 3 | 6 | no | — |
| 62 | C3×D3×D4 | — | 6 | 3 | no | — |
| 63 | #3811 | — | 6 | 3 | no | — |
| 64 | D3×#67 | — | 6 | 6 | no | — |
| 65 | #3802 | — | 3 | 3 | no | — |
| 66 | D3×D12 | — | 3 | 6 | no | — |
| 67 | C4×D32 | — | 3 | 3 | no | — |
| 68 | C4×D32 | — | 6 | 3 | no | — |
| 69 | #3797 | — | 3 | 3 | no | — |
| 70 | #3797 | — | 6 | 3 | no | — |
| 71 | D3×Dic6 | — | 3 | 6 | no | — |
| 72 | D3×Dic6 | — | 6 | 6 | no | — |
| 73 | C32×SD16 | — | 2 | 3 | no | — |
| 74 | C32×SD16 | — | 4 | 1 | no | — |
| 75 | C32×SD16 | C2×D3 | 1 | 3 | yes | complemented |
| 76 | #3755 | C2×D3 | 1 | 3 | yes | complemented |
| 77 | #3754 | C2×D3 | 1 | 3 | yes | complemented |
| 78 | #3744 | C2×D3 | 1 | 3 | yes | complemented |
| 79 | C8×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 80 | C3×#215 | — | 3 | 6 | no | — |
| 81 | C3×#215 | — | 6 | 3 | no | — |
| 82 | C3×#214 | — | 3 | 6 | no | — |
| 83 | C3×#214 | — | 6 | 3 | no | — |
| 84 | C3×#204 | — | 3 | 6 | no | — |
| 85 | C3×#204 | — | 6 | 3 | no | — |
| 86 | C3×D3×C8 | — | 3 | 6 | no | — |
| 87 | C3×D3×C8 | — | 6 | 3 | no | — |
| 88 | #3717 | — | 3 | 6 | no | — |
| 89 | #3716 | — | 3 | 6 | no | — |
| 90 | #3715 | — | 3 | 6 | no | — |
| 91 | #3710 | — | 3 | 3 | no | — |
| 92 | D3×C3⋊C8 | — | 3 | 6 | no | — |
| 93 | C22×C33 | — | 2 | 1 | no | — |
| 94 | C2×C3×C3⋊D3 | — | 2 | 3 | no | — |
| 95 | C2×C3×C3⋊D3 | — | 4 | 6 | no | — |
| 96 | C2×C3×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 97 | #1113 | — | 4 | 6 | no | — |
| 98 | #1113 | SD16 | 1 | 4 | yes | direct product factor |
| 99 | C33×C4 | — | 2 | 1 | no | — |
| 100 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 101 | C3×C3⋊Dic3 | — | 2 | 3 | no | — |
| 102 | C3×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 103 | C2×D3×Q8 | — | 9 | 3 | no | — |
| 104 | C2×D3×D4 | — | 9 | 3 | no | — |
| 105 | C2×C3×SD16 | — | 9 | 3 | no | — |
| 106 | C2×#215 | — | 9 | 3 | no | — |
| 107 | C2×#214 | — | 9 | 3 | no | — |
| 108 | D3×SD16 | — | 3 | 6 | no | — |
| 109 | D3×SD16 | — | 6 | 3 | no | — |
| 110 | D3×SD16 | — | 9 | 6 | no | — |
| 111 | D3×SD16 | — | 9 | 6 | no | — |
| 112 | D3×SD16 | — | 9 | 6 | no | — |
| 113 | C2×#204 | — | 9 | 3 | no | — |
| 114 | C2×D3×C8 | — | 9 | 3 | no | — |
| 115 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 116 | C22×C3×D3 | — | 6 | 6 | no | — |
| 117 | C22×C3×D3 | — | 12 | 3 | no | — |
| 118 | C2×D32 | — | 3 | 3 | no | — |
| 119 | C2×D32 | — | 6 | 6 | no | — |
| 120 | C2×D32 | — | 6 | 3 | no | — |
| 121 | C2×D32 | — | 12 | 12 | no | — |
| 122 | C32×Q8 | — | 2 | 3 | no | — |
| 123 | C32×Q8 | — | 4 | 1 | no | — |
| 124 | C32×Q8 | C22×D3 | 1 | 3 | yes | complemented |
| 125 | C32×D4 | — | 2 | 3 | no | — |
| 126 | C32×D4 | — | 4 | 1 | no | — |
| 127 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 128 | #638 | — | 2 | 3 | no | — |
| 129 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 130 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 131 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 132 | #634 | — | 2 | 3 | no | — |
| 133 | #634 | C22×D3 | 1 | 3 | yes | complemented |
| 134 | C3×#67 | — | 6 | 6 | no | — |
| 135 | C3×#67 | — | 12 | 3 | no | — |
| 136 | C3×D12 | — | 3 | 6 | no | — |
| 137 | C3×D12 | — | 6 | 3 | no | — |
| 138 | C3×C4×D3 | — | 3 | 6 | no | — |
| 139 | C3×C4×D3 | — | 6 | 3 | no | — |
| 140 | C3×C4×D3 | — | 6 | 6 | no | — |
| 141 | C3×C4×D3 | — | 12 | 3 | no | — |
| 142 | C3×Dic6 | — | 3 | 6 | no | — |
| 143 | C3×Dic6 | — | 6 | 3 | no | — |
| 144 | C3×Dic6 | — | 6 | 6 | no | — |
| 145 | C3×Dic6 | — | 12 | 3 | no | — |
| 146 | #627 | — | 6 | 6 | no | — |
| 147 | #627 | — | 6 | 3 | no | — |
| 148 | #626 | — | 6 | 6 | no | — |
| 149 | #625 | — | 6 | 3 | no | — |
| 150 | #624 | — | 3 | 3 | no | — |
| 151 | #624 | — | 6 | 3 | no | — |
| 152 | D3×Dic3 | — | 3 | 6 | no | — |
| 153 | D3×Dic3 | — | 6 | 6 | no | — |
| 154 | C32×C8 | — | 2 | 3 | no | — |
| 155 | C32×C8 | — | 4 | 1 | no | — |
| 156 | C32×C8 | C22×D3 | 1 | 3 | yes | complemented |
| 157 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | complemented |
| 158 | C3×C3⋊C8 | — | 3 | 6 | no | — |
| 159 | C3×C3⋊C8 | — | 6 | 3 | no | — |
| 160 | C22×SD16 | — | 27 | 1 | no | Sylow |
| 161 | C2×C33 | — | 4 | 1 | no | — |
| 162 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 163 | C3×C3⋊D3 | — | 4 | 3 | no | — |
| 164 | C3×C3⋊D3 | C2×SD16 | 1 | 6 | yes | complemented |
| 165 | C23×D3 | — | 18 | 3 | no | — |
| 166 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 167 | C2×C3×D4 | — | 9 | 3 | no | — |
| 168 | C2×#67 | — | 18 | 3 | no | — |
| 169 | D3×Q8 | — | 3 | 6 | no | — |
| 170 | D3×Q8 | — | 6 | 3 | no | — |
| 171 | D3×Q8 | — | 9 | 6 | no | — |
| 172 | D3×Q8 | — | 18 | 6 | no | — |
| 173 | D3×D4 | — | 3 | 6 | no | — |
| 174 | D3×D4 | — | 6 | 3 | no | — |
| 175 | D3×D4 | — | 9 | 6 | no | — |
| 176 | D3×D4 | — | 18 | 6 | no | — |
| 177 | C2×D12 | — | 9 | 3 | no | — |
| 178 | C2×C4×D3 | — | 9 | 3 | no | — |
| 179 | C2×C4×D3 | — | 18 | 3 | no | — |
| 180 | C2×Dic6 | — | 9 | 3 | no | — |
| 181 | C2×Dic6 | — | 18 | 3 | no | — |
| 182 | C3×SD16 | — | 2 | 3 | no | — |
| 183 | C3×SD16 | — | 4 | 1 | no | — |
| 184 | C3×SD16 | — | 9 | 3 | no | — |
| 185 | C3×SD16 | — | 9 | 3 | no | — |
| 186 | C3×SD16 | — | 9 | 3 | no | — |
| 187 | C3×SD16 | D32 | 1 | 3 | yes | complemented |
| 188 | C2×C3×C8 | — | 9 | 3 | no | — |
| 189 | #215 | — | 3 | 6 | no | — |
| 190 | #215 | — | 6 | 3 | no | — |
| 191 | #215 | — | 9 | 6 | no | — |
| 192 | #214 | — | 3 | 6 | no | — |
| 193 | #214 | — | 6 | 3 | no | — |
| 194 | #214 | — | 9 | 6 | no | — |
| 195 | C2×C3⋊C8 | — | 9 | 3 | no | — |
| 196 | #204 | — | 3 | 6 | no | — |
| 197 | #204 | — | 6 | 3 | no | — |
| 198 | #204 | — | 9 | 6 | no | — |
| 199 | D3×C8 | — | 3 | 6 | no | — |
| 200 | D3×C8 | — | 6 | 3 | no | — |
| 201 | D3×C8 | — | 9 | 6 | no | — |
| 202 | C22×C32 | — | 2 | 3 | no | — |
| 203 | C22×C32 | — | 4 | 3 | no | — |
| 204 | C22×C32 | — | 8 | 1 | no | — |
| 205 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 206 | C2×C3⋊D3 | — | 4 | 6 | no | — |
| 207 | C2×C3⋊D3 | D3×D4 | 1 | 3 | yes | — |
| 208 | C2×C3×D3 | — | 3 | 6 | no | — |
| 209 | C2×C3×D3 | — | 6 | 3 | no | — |
| 210 | C2×C3×D3 | — | 6 | 6 | no | — |
| 211 | C2×C3×D3 | — | 12 | 3 | no | — |
| 212 | C2×C3×D3 | — | 12 | 12 | no | — |
| 213 | C2×C3×D3 | — | 24 | 6 | no | — |
| 214 | D32 | — | 3 | 12 | no | — |
| 215 | D32 | — | 12 | 12 | no | — |
| 216 | D32 | — | 12 | 6 | no | — |
| 217 | C32×C4 | — | 2 | 3 | no | — |
| 218 | C32×C4 | — | 2 | 3 | no | — |
| 219 | C32×C4 | — | 4 | 1 | no | — |
| 220 | C32×C4 | — | 4 | 3 | no | — |
| 221 | C32×C4 | — | 8 | 1 | no | — |
| 222 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 223 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 224 | C3⋊Dic3 | D3×D4 | 1 | 3 | yes | — |
| 225 | C3×Dic3 | — | 3 | 6 | no | — |
| 226 | C3×Dic3 | — | 6 | 3 | no | — |
| 227 | C3×Dic3 | — | 6 | 6 | no | — |
| 228 | C3×Dic3 | — | 12 | 3 | no | — |
| 229 | C22×Q8 | — | 27 | 1 | no | — |
| 230 | C22×D4 | — | 27 | 1 | no | — |
| 231 | C2×SD16 | — | 9 | 3 | no | — |
| 232 | C2×SD16 | — | 27 | 3 | no | — |
| 233 | C2×SD16 | — | 27 | 3 | no | — |
| 234 | C2×SD16 | — | 27 | 3 | no | — |
| 235 | C22×C8 | — | 27 | 1 | no | — |
| 236 | C33 | C22×SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 237 | C23×C3 | — | 18 | 3 | no | — |
| 238 | C22×D3 | — | 6 | 6 | no | — |
| 239 | C22×D3 | — | 9 | 3 | no | — |
| 240 | C22×D3 | — | 12 | 3 | no | — |
| 241 | C22×D3 | — | 18 | 6 | no | — |
| 242 | C22×D3 | — | 18 | 3 | no | — |
| 243 | C22×D3 | — | 36 | 12 | no | — |
| 244 | C3×Q8 | — | 2 | 3 | no | — |
| 245 | C3×Q8 | — | 4 | 1 | no | — |
| 246 | C3×Q8 | — | 9 | 3 | no | — |
| 247 | C3×Q8 | — | 18 | 3 | no | — |
| 248 | C3×Q8 | C2×D32 | 1 | 3 | yes | complemented |
| 249 | C3×D4 | — | 2 | 3 | no | — |
| 250 | C3×D4 | — | 4 | 1 | no | — |
| 251 | C3×D4 | — | 9 | 3 | no | — |
| 252 | C3×D4 | — | 18 | 3 | no | — |
| 253 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 254 | C2×C3×C4 | — | 9 | 3 | no | — |
| 255 | C2×C3×C4 | — | 18 | 3 | no | — |
| 256 | #67 | — | 6 | 6 | no | — |
| 257 | #67 | — | 12 | 3 | no | — |
| 258 | #67 | — | 18 | 6 | no | — |
| 259 | C2×Dic3 | — | 9 | 3 | no | — |
| 260 | C2×Dic3 | — | 18 | 3 | no | — |
| 261 | D12 | — | 3 | 6 | no | — |
| 262 | D12 | — | 6 | 3 | no | — |
| 263 | D12 | — | 18 | 3 | no | — |
| 264 | C4×D3 | — | 3 | 6 | no | — |
| 265 | C4×D3 | — | 6 | 3 | no | — |
| 266 | C4×D3 | — | 6 | 6 | no | — |
| 267 | C4×D3 | — | 9 | 6 | no | — |
| 268 | C4×D3 | — | 12 | 3 | no | — |
| 269 | C4×D3 | — | 18 | 6 | no | — |
| 270 | Dic6 | — | 3 | 6 | no | — |
| 271 | Dic6 | — | 6 | 3 | no | — |
| 272 | Dic6 | — | 6 | 6 | no | — |
| 273 | Dic6 | — | 12 | 3 | no | — |
| 274 | Dic6 | — | 18 | 6 | no | — |
| 275 | Dic6 | — | 18 | 3 | no | — |
| 276 | C3×C8 | — | 2 | 3 | no | — |
| 277 | C3×C8 | — | 4 | 1 | no | — |
| 278 | C3×C8 | — | 9 | 3 | no | — |
| 279 | C3×C8 | C2×D32 | 1 | 3 | yes | complemented |
| 280 | C3⋊C8 | — | 3 | 6 | no | — |
| 281 | C3⋊C8 | — | 6 | 3 | no | — |
| 282 | C2×C32 | — | 2 | 3 | no | — |
| 283 | C2×C32 | — | 4 | 1 | no | — |
| 284 | C2×C32 | — | 4 | 3 | no | — |
| 285 | C2×C32 | — | 8 | 3 | no | — |
| 286 | C2×C32 | — | 16 | 1 | no | — |
| 287 | C2×C32 | C2×D3×D4 | 1 | 3 | yes | — |
| 288 | C3⋊D3 | — | 4 | 3 | no | — |
| 289 | C3⋊D3 | D3×SD16 | 1 | 6 | yes | complemented |
| 290 | C3×D3 | — | 3 | 12 | no | — |
| 291 | C3×D3 | — | 6 | 6 | no | — |
| 292 | C3×D3 | — | 12 | 6 | no | — |
| 293 | C3×D3 | — | 24 | 3 | no | — |
| 294 | C24 | — | 54 | 1 | no | — |
| 295 | C2×Q8 | — | 9 | 3 | no | — |
| 296 | C2×Q8 | — | 27 | 3 | no | — |
| 297 | C2×Q8 | — | 54 | 3 | no | — |
| 298 | C2×D4 | — | 9 | 3 | no | — |
| 299 | C2×D4 | — | 27 | 3 | no | — |
| 300 | C2×D4 | — | 54 | 3 | no | — |
| 301 | C22×C4 | — | 27 | 1 | no | — |
| 302 | C22×C4 | — | 54 | 1 | no | — |
| 303 | SD16 | — | 9 | 3 | no | — |
| 304 | SD16 | — | 9 | 3 | no | — |
| 305 | SD16 | — | 9 | 3 | no | — |
| 306 | SD16 | — | 27 | 6 | no | — |
| 307 | SD16 | #1113 | 1 | 1 | yes | characteristic, direct product factor |
| 308 | C2×C8 | — | 9 | 3 | no | — |
| 309 | C2×C8 | — | 27 | 3 | no | — |
| 310 | C22×C3 | — | 2 | 3 | no | — |
| 311 | C22×C3 | — | 4 | 3 | no | — |
| 312 | C22×C3 | — | 8 | 1 | no | — |
| 313 | C22×C3 | — | 9 | 3 | no | — |
| 314 | C22×C3 | — | 18 | 3 | no | — |
| 315 | C22×C3 | — | 36 | 6 | no | — |
| 316 | C2×D3 | — | 3 | 6 | no | — |
| 317 | C2×D3 | — | 6 | 3 | no | — |
| 318 | C2×D3 | — | 6 | 6 | no | — |
| 319 | C2×D3 | — | 9 | 12 | no | — |
| 320 | C2×D3 | — | 12 | 3 | no | — |
| 321 | C2×D3 | — | 12 | 12 | no | — |
| 322 | C2×D3 | — | 24 | 6 | no | — |
| 323 | C2×D3 | — | 36 | 12 | no | — |
| 324 | C2×D3 | — | 36 | 6 | no | — |
| 325 | C3×C4 | — | 2 | 3 | no | — |
| 326 | C3×C4 | — | 2 | 3 | no | — |
| 327 | C3×C4 | — | 4 | 3 | no | — |
| 328 | C3×C4 | — | 4 | 1 | no | — |
| 329 | C3×C4 | — | 8 | 1 | no | — |
| 330 | C3×C4 | — | 9 | 3 | no | — |
| 331 | C3×C4 | — | 18 | 3 | no | — |
| 332 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 333 | Dic3 | — | 3 | 6 | no | — |
| 334 | Dic3 | — | 6 | 3 | no | — |
| 335 | Dic3 | — | 6 | 6 | no | — |
| 336 | Dic3 | — | 12 | 3 | no | — |
| 337 | C32 | — | 2 | 3 | no | — |
| 338 | C32 | — | 4 | 1 | no | — |
| 339 | C32 | C2×D3×SD16 | 1 | 3 | yes | complemented |
| 340 | C23 | — | 18 | 3 | no | — |
| 341 | C23 | — | 27 | 1 | no | — |
| 342 | C23 | — | 54 | 3 | no | — |
| 343 | C23 | — | 108 | 4 | no | — |
| 344 | Q8 | — | 9 | 3 | no | — |
| 345 | Q8 | — | 18 | 3 | no | — |
| 346 | Q8 | — | 54 | 3 | no | — |
| 347 | Q8 | C2×#1113 | 1 | 1 | yes | characteristic, complemented |
| 348 | D4 | — | 9 | 3 | no | — |
| 349 | D4 | — | 18 | 3 | no | — |
| 350 | D4 | — | 54 | 3 | no | — |
| 351 | D4 | C2×#1113 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | — | 9 | 3 | no | — |
| 353 | C2×C4 | — | 18 | 3 | no | — |
| 354 | C2×C4 | — | 27 | 3 | no | — |
| 355 | C2×C4 | — | 54 | 3 | no | — |
| 356 | C8 | — | 9 | 3 | no | — |
| 357 | C8 | C2×#1113 | 1 | 1 | yes | characteristic, complemented |
| 358 | C2×C3 | — | 2 | 3 | no | — |
| 359 | C2×C3 | — | 4 | 3 | no | — |
| 360 | C2×C3 | — | 4 | 1 | no | — |
| 361 | C2×C3 | — | 8 | 3 | no | — |
| 362 | C2×C3 | — | 9 | 6 | no | — |
| 363 | C2×C3 | — | 16 | 1 | no | — |
| 364 | C2×C3 | — | 36 | 3 | no | — |
| 365 | C2×C3 | D32×D4 | 1 | 3 | yes | — |
| 366 | D3 | — | 3 | 12 | no | — |
| 367 | D3 | — | 6 | 6 | no | — |
| 368 | D3 | — | 12 | 6 | no | — |
| 369 | D3 | — | 24 | 3 | no | — |
| 370 | C22 | — | 2 | 1 | no | — |
| 371 | C22 | — | 9 | 3 | no | — |
| 372 | C22 | — | 18 | 3 | no | — |
| 373 | C22 | — | 27 | 4 | no | — |
| 374 | C22 | — | 36 | 6 | no | — |
| 375 | C22 | — | 108 | 6 | no | — |
| 376 | C4 | — | 2 | 1 | no | — |
| 377 | C4 | — | 9 | 3 | no | — |
| 378 | C4 | — | 18 | 3 | no | — |
| 379 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 380 | C3 | — | 2 | 3 | no | — |
| 381 | C3 | — | 4 | 1 | no | — |
| 382 | C3 | D32×SD16 | 1 | 3 | yes | complemented |
| 383 | C2 | — | 4 | 1 | no | — |
| 384 | C2 | — | 9 | 6 | no | — |
| 385 | C2 | — | 36 | 3 | no | — |
| 386 | C2 | D4×#1113 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#1113 | C2 | semidirect |
| 3. C3×SD16×C3⋊D3 | C2 | semidirect |
| 4. #11723708 | C2 | semidirect |
| 5. #11723704 | C2 | semidirect |
| 6. #11723646 | C2 | semidirect |
| 7. C8×#1113 | C2 | semidirect |
| 10. C3×Q8×C3⋊D3 | C22 | semidirect |
| 17. #89040 | C22 | semidirect |
| 18. C33×SD16 | C22 | semidirect |
| 19. C3×#3755 | C22 | semidirect |
| 20. C3×#3754 | C22 | semidirect |
| 21. C3×#3744 | C22 | semidirect |
| 22. C3×C8×C3⋊D3 | C22 | semidirect |
| 23. #88811 | C22 | semidirect |
| 24. #88808 | C22 | semidirect |
| 27. SD16×C3⋊D3 | D3 | semidirect |
| 41. C33×Q8 | C23 | semidirect |
| 48. C3×#634 | C23 | semidirect |
| 53. C33×C8 | C23 | semidirect |
| 54. C3×C3⋊(C3⋊C8) | C23 | semidirect |
| 57. Q8×C3⋊D3 | C2×D3 | semidirect |
| 75. C32×SD16 | C2×D3 | semidirect |
| 76. #3755 | C2×D3 | semidirect |
| 77. #3754 | C2×D3 | semidirect |
| 78. #3744 | C2×D3 | semidirect |
| 79. C8×C3⋊D3 | C2×D3 | semidirect |
| 98. #1113 | SD16 | direct (N × H) |
| 124. C32×Q8 | C22×D3 | semidirect |
| 133. #634 | C22×D3 | semidirect |
| 156. C32×C8 | C22×D3 | semidirect |
| 157. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 164. C3×C3⋊D3 | C2×SD16 | semidirect |
| 187. C3×SD16 | D32 | semidirect |
| 236. C33 | C22×SD16 | semidirect |
| 248. C3×Q8 | C2×D32 | semidirect |
| 279. C3×C8 | C2×D32 | semidirect |
| 289. C3⋊D3 | D3×SD16 | semidirect |
| 307. SD16 | #1113 | direct (N × H) |
| 339. C32 | C2×D3×SD16 | semidirect |
| 347. Q8 | C2×#1113 | semidirect |
| 357. C8 | C2×#1113 | semidirect |
| 382. C3 | D32×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1113 | 2 |
| D4×#1113 | 2 |
| C3×SD16×C3⋊D3 | 2 |
| #11723708 | 2 |
| #11723704 | 2 |
| #11723646 | 2 |
| C8×#1113 | 2 |
| D32×SD16 | 3 |