Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
735 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 735 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C22×D3×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10593654 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3×#859 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10593209 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#5420 | — | 3 | 1 | no | maximal |
| 7 | D3×#419 | — | 3 | 1 | no | maximal |
| 8 | C22×C3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×D3×SL(2,𝔽3) | C4 | 1 | 4 | yes | complemented |
| 10 | C2×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 12 | D3×#217 | — | 4 | 1 | no | maximal |
| 13 | C3⋊#859 | C22 | 1 | 2 | yes | complemented |
| 14 | C3×#859 | C22 | 1 | 2 | yes | complemented |
| 15 | C22×D3×Q8 | D3 | 1 | 1 | yes | characteristic |
| 16 | C23×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 17 | C2×D3×M16 | — | 3 | 1 | no | — |
| 18 | D3×#117 | — | 3 | 1 | no | — |
| 19 | #5420 | — | 3 | 1 | no | — |
| 20 | #5420 | — | 3 | 2 | no | — |
| 21 | #5420 | — | 6 | 1 | no | — |
| 22 | #5420 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 23 | C2×#859 | — | 3 | 2 | no | — |
| 24 | C3×#419 | — | 3 | 1 | no | — |
| 25 | #5225 | — | 3 | 1 | no | — |
| 26 | #5120 | — | 3 | 1 | no | — |
| 27 | #5004 | — | 3 | 1 | no | — |
| 28 | #4802 | — | 3 | 2 | no | — |
| 29 | #4802 | — | 3 | 2 | no | — |
| 30 | D3×#103 | — | 3 | 2 | no | — |
| 31 | D3×#103 | — | 3 | 2 | no | — |
| 32 | C23×C3×D3 | — | 4 | 1 | no | — |
| 33 | C2×C3×SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 34 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×D3×Dic3 | — | 4 | 2 | no | — |
| 36 | D3×SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | — |
| 37 | D3×SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 38 | #3757 | — | 4 | 1 | no | — |
| 39 | C3×#217 | — | 4 | 1 | no | — |
| 40 | (C2×D3)⋊Dic3 | — | 4 | 2 | no | — |
| 41 | C2×#419 | — | 9 | 1 | no | Sylow |
| 42 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 44 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 45 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 46 | C2×D3×Q8 | Dic3 | 1 | 4 | yes | complemented |
| 47 | C2×D3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 48 | C2×D3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 49 | C22×C4×D3 | — | 3 | 1 | no | — |
| 50 | C22×Dic6 | — | 3 | 1 | no | — |
| 51 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 52 | C22×SL(2,𝔽3) | — | 3 | 4 | no | — |
| 53 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 54 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 55 | C22×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×M16 | — | 3 | 1 | no | — |
| 57 | C3×#117 | — | 3 | 1 | no | — |
| 58 | C2×#217 | — | 12 | 1 | no | — |
| 59 | #926 | — | 3 | 1 | no | — |
| 60 | C2×#208 | — | 3 | 1 | no | — |
| 61 | D3×M16 | — | 6 | 4 | no | — |
| 62 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 63 | C2×D3×C8 | — | 3 | 2 | no | — |
| 64 | #892 | — | 3 | 2 | no | — |
| 65 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 66 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 67 | #877 | — | 6 | 1 | no | — |
| 68 | #872 | — | 6 | 1 | no | — |
| 69 | C42×D3 | — | 6 | 1 | no | — |
| 70 | #859 | — | 3 | 2 | no | — |
| 71 | #859 | — | 6 | 2 | no | — |
| 72 | #859 | C2×D3 | 1 | 2 | yes | complemented |
| 73 | C3×#103 | — | 3 | 2 | no | — |
| 74 | C3×#103 | — | 3 | 2 | no | — |
| 75 | #835 | — | 3 | 2 | no | — |
| 76 | #835 | — | 3 | 2 | no | — |
| 77 | #816 | — | 3 | 2 | no | — |
| 78 | #816 | — | 3 | 2 | no | — |
| 79 | #810 | — | 3 | 2 | no | — |
| 80 | #810 | — | 3 | 2 | no | — |
| 81 | C23×C32 | — | 4 | 1 | no | — |
| 82 | C22×C3×D3 | — | 4 | 4 | no | — |
| 83 | C22×C3×D3 | — | 4 | 1 | no | — |
| 84 | C22×C3×D3 | — | 4 | 1 | no | — |
| 85 | C22×C3×D3 | — | 8 | 4 | no | — |
| 86 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 87 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 88 | C3×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | D3×Dic3 | — | 8 | 4 | no | — |
| 90 | C23×Q8 | — | 3 | 1 | no | — |
| 91 | C22×M16 | — | 9 | 1 | no | — |
| 92 | C2×#117 | — | 9 | 1 | no | — |
| 93 | #419 | — | 3 | 1 | no | — |
| 94 | #419 | — | 9 | 2 | no | — |
| 95 | #419 | — | 9 | 2 | no | — |
| 96 | #419 | — | 9 | 1 | no | — |
| 97 | #419 | — | 9 | 1 | no | — |
| 98 | #419 | — | 9 | 1 | no | — |
| 99 | C2×#103 | — | 9 | 2 | no | — |
| 100 | C2×#103 | — | 9 | 2 | no | — |
| 101 | C24×C3 | — | 12 | 1 | no | — |
| 102 | C23×D3 | S4 | 1 | 1 | yes | characteristic |
| 103 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 104 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 105 | C2×C3×Q8 | C2×Dic3 | 1 | 2 | yes | complemented |
| 106 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 107 | C22×C3×C4 | — | 3 | 1 | no | — |
| 108 | C22×Dic3 | — | 3 | 1 | no | — |
| 109 | C22×Dic3 | — | 12 | 2 | no | — |
| 110 | D3×Q8 | — | 3 | 4 | no | — |
| 111 | D3×Q8 | — | 3 | 4 | no | — |
| 112 | D3×Q8 | — | 3 | 2 | no | — |
| 113 | D3×Q8 | — | 3 | 2 | no | — |
| 114 | D3×Q8 | — | 6 | 2 | no | — |
| 115 | D3×Q8 | — | 6 | 2 | no | — |
| 116 | D3×Q8 | C2×Dic3 | 1 | 2 | yes | — |
| 117 | D3×Q8 | C2×Dic3 | 1 | 2 | yes | complemented |
| 118 | C2×C4×D3 | — | 3 | 4 | no | — |
| 119 | C2×C4×D3 | — | 3 | 4 | no | — |
| 120 | C2×C4×D3 | — | 3 | 1 | no | — |
| 121 | C2×C4×D3 | — | 3 | 1 | no | — |
| 122 | C2×C4×D3 | — | 3 | 1 | no | — |
| 123 | C2×C4×D3 | — | 3 | 1 | no | — |
| 124 | C2×C4×D3 | — | 6 | 2 | no | — |
| 125 | C2×Dic6 | — | 3 | 1 | no | — |
| 126 | C2×Dic6 | — | 3 | 1 | no | — |
| 127 | C2×Dic6 | — | 3 | 4 | no | — |
| 128 | C2×Dic6 | — | 6 | 2 | no | — |
| 129 | C2×Dic6 | — | 6 | 1 | no | — |
| 130 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 131 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 132 | C2×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 133 | C2×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 134 | C2×SL(2,𝔽3) | C4×D3 | 1 | 2 | yes | complemented |
| 135 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 136 | C3×M16 | — | 6 | 2 | no | — |
| 137 | C2×C3×C8 | — | 3 | 2 | no | — |
| 138 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 139 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 140 | C3×C42 | — | 6 | 1 | no | — |
| 141 | #217 | — | 4 | 1 | no | — |
| 142 | #217 | — | 6 | 1 | no | — |
| 143 | #217 | — | 12 | 2 | no | — |
| 144 | #217 | — | 12 | 1 | no | — |
| 145 | #217 | — | 24 | 1 | no | — |
| 146 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 147 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 148 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 149 | C4×Dic3 | — | 6 | 2 | no | — |
| 150 | C4×Dic3 | — | 6 | 1 | no | — |
| 151 | #208 | — | 6 | 2 | no | — |
| 152 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 153 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 154 | D3×C8 | — | 6 | 4 | no | — |
| 155 | C22×C32 | — | 4 | 2 | no | — |
| 156 | C22×C32 | — | 4 | 1 | no | — |
| 157 | C22×C32 | — | 8 | 2 | no | — |
| 158 | C2×C3×D3 | — | 4 | 4 | no | — |
| 159 | C2×C3×D3 | — | 4 | 2 | no | — |
| 160 | C2×C3×D3 | — | 4 | 2 | no | — |
| 161 | C2×C3×D3 | — | 8 | 8 | no | — |
| 162 | C2×C3×D3 | — | 8 | 2 | no | — |
| 163 | C3⋊Dic3 | — | 8 | 2 | no | — |
| 164 | C3×Dic3 | — | 8 | 2 | no | — |
| 165 | C22×Q8 | — | 3 | 4 | no | — |
| 166 | C22×Q8 | — | 3 | 1 | no | — |
| 167 | C22×Q8 | — | 3 | 1 | no | — |
| 168 | C22×Q8 | — | 9 | 1 | no | — |
| 169 | C22×Q8 | — | 9 | 1 | no | — |
| 170 | C22×Q8 | — | 9 | 1 | no | — |
| 171 | C22×Q8 | — | 9 | 4 | no | — |
| 172 | C22×Q8 | D32 | 1 | 1 | yes | characteristic |
| 173 | C23×C4 | — | 9 | 1 | no | — |
| 174 | C2×M16 | — | 3 | 1 | no | — |
| 175 | C2×M16 | — | 9 | 2 | no | — |
| 176 | C2×M16 | — | 9 | 1 | no | — |
| 177 | C2×M16 | — | 18 | 4 | no | — |
| 178 | C22×C8 | — | 9 | 2 | no | — |
| 179 | #117 | — | 3 | 1 | no | — |
| 180 | #117 | — | 9 | 2 | no | — |
| 181 | #117 | — | 9 | 1 | no | — |
| 182 | #117 | — | 18 | 1 | no | — |
| 183 | #117 | — | 18 | 1 | no | — |
| 184 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 185 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 186 | C2×C42 | — | 18 | 1 | no | — |
| 187 | #103 | — | 3 | 2 | no | — |
| 188 | #103 | — | 3 | 2 | no | — |
| 189 | #103 | — | 9 | 2 | no | — |
| 190 | #103 | — | 9 | 2 | no | — |
| 191 | #103 | — | 9 | 2 | no | — |
| 192 | #103 | — | 9 | 2 | no | — |
| 193 | #103 | — | 9 | 2 | no | — |
| 194 | #103 | — | 9 | 2 | no | — |
| 195 | C23×C3 | — | 4 | 1 | no | — |
| 196 | C23×C3 | — | 8 | 1 | no | — |
| 197 | C23×C3 | — | 12 | 1 | no | — |
| 198 | C23×C3 | — | 12 | 1 | no | — |
| 199 | C23×C3 | — | 12 | 4 | no | — |
| 200 | C23×C3 | — | 24 | 4 | no | — |
| 201 | C23×C3 | C2×S4 | 1 | 1 | yes | characteristic |
| 202 | C22×D3 | — | 2 | 4 | no | — |
| 203 | C22×D3 | SL(2,ℤ/4) | 1 | 4 | yes | — |
| 204 | C22×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 205 | C22×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 206 | C3×Q8 | — | 3 | 2 | no | — |
| 207 | C3×Q8 | — | 3 | 1 | no | — |
| 208 | C3×Q8 | — | 6 | 1 | no | — |
| 209 | C3×Q8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×C4 | — | 3 | 2 | no | — |
| 211 | C2×C3×C4 | — | 3 | 2 | no | — |
| 212 | C2×C3×C4 | — | 3 | 1 | no | — |
| 213 | C2×C3×C4 | — | 3 | 1 | no | — |
| 214 | C2×C3×C4 | — | 6 | 2 | no | — |
| 215 | C2×Dic3 | — | 3 | 4 | no | — |
| 216 | C2×Dic3 | — | 3 | 1 | no | — |
| 217 | C2×Dic3 | — | 3 | 1 | no | — |
| 218 | C2×Dic3 | — | 4 | 2 | no | — |
| 219 | C2×Dic3 | — | 6 | 2 | no | — |
| 220 | C2×Dic3 | — | 12 | 2 | no | — |
| 221 | C2×Dic3 | — | 24 | 2 | no | — |
| 222 | C2×Dic3 | — | 24 | 4 | no | — |
| 223 | C4×D3 | — | 3 | 2 | no | — |
| 224 | C4×D3 | — | 3 | 2 | no | — |
| 225 | C4×D3 | — | 3 | 2 | no | — |
| 226 | C4×D3 | — | 3 | 2 | no | — |
| 227 | C4×D3 | — | 3 | 4 | no | — |
| 228 | C4×D3 | — | 3 | 4 | no | — |
| 229 | C4×D3 | — | 12 | 4 | no | — |
| 230 | Dic6 | — | 3 | 2 | no | — |
| 231 | Dic6 | — | 3 | 2 | no | — |
| 232 | Dic6 | — | 6 | 1 | no | — |
| 233 | Dic6 | — | 6 | 1 | no | — |
| 234 | Dic6 | — | 6 | 4 | no | — |
| 235 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 236 | SL(2,𝔽3) | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 237 | C3×C8 | — | 6 | 2 | no | — |
| 238 | C3⋊C8 | — | 6 | 2 | no | — |
| 239 | C2×C32 | — | 4 | 2 | no | — |
| 240 | C2×C32 | — | 4 | 1 | no | — |
| 241 | C2×C32 | — | 8 | 2 | no | — |
| 242 | C3×D3 | — | 4 | 4 | no | — |
| 243 | C3×D3 | — | 8 | 2 | no | — |
| 244 | C24 | — | 3 | 1 | no | — |
| 245 | C2×Q8 | — | 3 | 1 | no | — |
| 246 | C2×Q8 | — | 3 | 2 | no | — |
| 247 | C2×Q8 | — | 3 | 2 | no | — |
| 248 | C2×Q8 | — | 3 | 2 | no | — |
| 249 | C2×Q8 | — | 9 | 1 | no | — |
| 250 | C2×Q8 | — | 9 | 1 | no | — |
| 251 | C2×Q8 | — | 9 | 4 | no | — |
| 252 | C2×Q8 | — | 9 | 2 | no | — |
| 253 | C2×Q8 | — | 9 | 2 | no | — |
| 254 | C2×Q8 | — | 9 | 4 | no | — |
| 255 | C2×Q8 | — | 9 | 4 | no | — |
| 256 | C2×Q8 | — | 18 | 1 | no | — |
| 257 | C2×Q8 | — | 18 | 2 | no | — |
| 258 | C2×Q8 | — | 18 | 2 | no | — |
| 259 | C2×Q8 | — | 18 | 2 | no | — |
| 260 | C2×Q8 | D3×Dic3 | 1 | 2 | yes | complemented |
| 261 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 262 | C22×C4 | — | 3 | 1 | no | — |
| 263 | C22×C4 | — | 9 | 1 | no | — |
| 264 | C22×C4 | — | 9 | 1 | no | — |
| 265 | C22×C4 | — | 9 | 1 | no | — |
| 266 | C22×C4 | — | 9 | 1 | no | — |
| 267 | C22×C4 | — | 9 | 4 | no | — |
| 268 | C22×C4 | — | 9 | 4 | no | — |
| 269 | C22×C4 | — | 9 | 1 | no | — |
| 270 | C22×C4 | — | 18 | 2 | no | — |
| 271 | M16 | — | 6 | 2 | no | — |
| 272 | M16 | — | 18 | 4 | no | — |
| 273 | M16 | — | 18 | 2 | no | — |
| 274 | C2×C8 | — | 3 | 2 | no | — |
| 275 | C2×C8 | — | 9 | 2 | no | — |
| 276 | C2×C8 | — | 18 | 4 | no | — |
| 277 | C4⋊C4 | — | 3 | 2 | no | — |
| 278 | C4⋊C4 | — | 9 | 2 | no | — |
| 279 | C4⋊C4 | — | 18 | 2 | no | — |
| 280 | C22⋊C4 | — | 6 | 1 | no | — |
| 281 | C22⋊C4 | — | 18 | 2 | no | — |
| 282 | C22⋊C4 | — | 18 | 1 | no | — |
| 283 | C42 | — | 6 | 1 | no | — |
| 284 | C42 | — | 18 | 1 | no | — |
| 285 | C42 | — | 18 | 2 | no | — |
| 286 | C22×C3 | — | 2 | 2 | no | — |
| 287 | C22×C3 | — | 4 | 1 | no | — |
| 288 | C22×C3 | — | 4 | 2 | no | — |
| 289 | C22×C3 | — | 8 | 2 | no | — |
| 290 | C22×C3 | — | 8 | 1 | no | — |
| 291 | C22×C3 | — | 8 | 2 | no | — |
| 292 | C22×C3 | — | 12 | 4 | no | — |
| 293 | C22×C3 | — | 12 | 2 | no | — |
| 294 | C22×C3 | — | 12 | 2 | no | — |
| 295 | C22×C3 | — | 16 | 2 | no | — |
| 296 | C22×C3 | — | 24 | 2 | no | — |
| 297 | C22×C3 | — | 24 | 8 | no | — |
| 298 | C22×C3 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 299 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 300 | C2×D3 | — | 2 | 2 | no | — |
| 301 | C2×D3 | — | 2 | 8 | no | — |
| 302 | C2×D3 | #983 | 1 | 4 | yes | — |
| 303 | C2×D3 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 304 | C2×D3 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 305 | C3×C4 | — | 3 | 1 | no | — |
| 306 | C3×C4 | — | 3 | 1 | no | — |
| 307 | C3×C4 | — | 3 | 2 | no | — |
| 308 | C3×C4 | — | 12 | 2 | no | — |
| 309 | Dic3 | — | 3 | 2 | no | — |
| 310 | Dic3 | — | 3 | 2 | no | — |
| 311 | Dic3 | — | 8 | 2 | no | — |
| 312 | Dic3 | — | 12 | 2 | no | — |
| 313 | Dic3 | — | 24 | 2 | no | — |
| 314 | Dic3 | — | 48 | 2 | no | — |
| 315 | C32 | — | 4 | 1 | no | Sylow |
| 316 | C23 | — | 3 | 1 | no | — |
| 317 | C23 | — | 3 | 1 | no | — |
| 318 | C23 | — | 3 | 4 | no | — |
| 319 | C23 | — | 6 | 4 | no | — |
| 320 | C23 | D3×S4 | 1 | 1 | yes | characteristic |
| 321 | Q8 | — | 3 | 2 | no | — |
| 322 | Q8 | — | 3 | 1 | no | — |
| 323 | Q8 | — | 6 | 1 | no | — |
| 324 | Q8 | — | 9 | 2 | no | — |
| 325 | Q8 | — | 9 | 2 | no | — |
| 326 | Q8 | — | 18 | 1 | no | — |
| 327 | Q8 | — | 18 | 1 | no | — |
| 328 | Q8 | — | 18 | 4 | no | — |
| 329 | Q8 | C2×D3×Dic3 | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | — | 3 | 1 | no | — |
| 331 | C2×C4 | — | 3 | 1 | no | — |
| 332 | C2×C4 | — | 3 | 2 | no | — |
| 333 | C2×C4 | — | 3 | 2 | no | — |
| 334 | C2×C4 | — | 6 | 2 | no | — |
| 335 | C2×C4 | — | 9 | 2 | no | — |
| 336 | C2×C4 | — | 9 | 2 | no | — |
| 337 | C2×C4 | — | 9 | 2 | no | — |
| 338 | C2×C4 | — | 9 | 2 | no | — |
| 339 | C2×C4 | — | 9 | 4 | no | — |
| 340 | C2×C4 | — | 9 | 4 | no | — |
| 341 | C2×C4 | — | 9 | 1 | no | — |
| 342 | C2×C4 | — | 9 | 1 | no | — |
| 343 | C2×C4 | — | 9 | 4 | no | — |
| 344 | C2×C4 | — | 18 | 2 | no | — |
| 345 | C2×C4 | — | 36 | 4 | no | — |
| 346 | C8 | — | 6 | 2 | no | — |
| 347 | C8 | — | 18 | 2 | no | — |
| 348 | C2×C3 | — | 2 | 2 | no | — |
| 349 | C2×C3 | — | 4 | 2 | no | — |
| 350 | C2×C3 | — | 4 | 1 | no | — |
| 351 | C2×C3 | — | 8 | 2 | no | — |
| 352 | C2×C3 | — | 8 | 2 | no | — |
| 353 | C2×C3 | — | 8 | 1 | no | — |
| 354 | C2×C3 | — | 12 | 4 | no | — |
| 355 | C2×C3 | — | 16 | 2 | no | — |
| 356 | C2×C3 | — | 24 | 2 | no | — |
| 357 | C2×C3 | C2×#983 | 1 | 2 | yes | — |
| 358 | C2×C3 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 359 | D3 | — | 2 | 2 | no | — |
| 360 | D3 | #5420 | 1 | 4 | yes | direct product factor |
| 361 | C22 | — | 2 | 2 | no | — |
| 362 | C22 | — | 3 | 4 | no | — |
| 363 | C22 | — | 3 | 2 | no | — |
| 364 | C22 | — | 3 | 2 | no | — |
| 365 | C22 | — | 6 | 8 | no | — |
| 366 | C22 | — | 6 | 2 | no | — |
| 367 | C22 | D3×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 368 | C22 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 369 | C4 | — | 3 | 1 | no | — |
| 370 | C4 | — | 3 | 1 | no | — |
| 371 | C4 | — | 3 | 2 | no | — |
| 372 | C4 | — | 9 | 2 | no | — |
| 373 | C4 | — | 9 | 2 | no | — |
| 374 | C4 | — | 12 | 2 | no | — |
| 375 | C4 | — | 36 | 2 | no | — |
| 376 | C3 | — | 4 | 1 | no | — |
| 377 | C3 | — | 8 | 1 | no | — |
| 378 | C3 | C2×#5420 | 1 | 1 | yes | characteristic, complemented |
| 379 | C2 | — | 2 | 2 | no | — |
| 380 | C2 | — | 3 | 4 | no | — |
| 381 | C2 | — | 6 | 2 | no | — |
| 382 | C2 | D3×#983 | 1 | 2 | yes | — |
| 383 | C2 | C2×D3×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10593654 | C2 | semidirect |
| 3. C3×#5420 | C2 | semidirect |
| 4. D3×#859 | C2 | semidirect |
| 5. #10593209 | C2 | semidirect |
| 9. C2×D3×SL(2,𝔽3) | C4 | semidirect |
| 13. C3⋊#859 | C22 | semidirect |
| 14. C3×#859 | C22 | semidirect |
| 22. #5420 | D3 | direct (N × H) |
| 33. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 37. D3×SL(2,𝔽3) | C2×C4 | semidirect |
| 46. C2×D3×Q8 | Dic3 | semidirect |
| 72. #859 | C2×D3 | semidirect |
| 105. C2×C3×Q8 | C2×Dic3 | semidirect |
| 117. D3×Q8 | C2×Dic3 | semidirect |
| 134. C2×SL(2,𝔽3) | C4×D3 | semidirect |
| 260. C2×Q8 | D3×Dic3 | semidirect |
| 360. D3 | #5420 | direct (N × H) |
| 378. C3 | C2×#5420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×SL(2,𝔽3) | 2 |
| #10593654 | 2 |
| C3×#5420 | 2 |
| D3×#859 | 2 |
| #10593209 | 2 |
| C2×#5420 | 3 |
| D3×#419 | 3 |
| D3×#217 | 4 |