Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
372 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 51 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×C3⋊#157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11724302 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11723710 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#63944 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11722763 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11722760 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11722759 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10593477 | — | 3 | 1 | no | maximal |
| 9 | C3×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #89040 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#3797 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4⋊(C3⋊#157) | — | 2 | 1 | no | — |
| 13 | C4⋊(C3⋊#157) | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×C3⋊#157 | — | 2 | 1 | no | — |
| 15 | C4×C3⋊#157 | C22 | 1 | 1 | yes | characteristic |
| 16 | #88934 | — | 2 | 1 | no | — |
| 17 | #88934 | — | 2 | 1 | no | — |
| 18 | C3×#3756 | — | 2 | 1 | no | — |
| 19 | C32×#216 | — | 2 | 1 | no | — |
| 20 | #88812 | — | 2 | 1 | no | — |
| 21 | #88808 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#3719 | — | 2 | 1 | no | — |
| 23 | C3×#3710 | C22 | 1 | 1 | yes | characteristic |
| 24 | Q8×#157 | — | 3 | 1 | no | — |
| 25 | #64222 | — | 3 | 1 | no | — |
| 26 | C3×D3×Q16 | — | 6 | 1 | no | — |
| 27 | #63944 | — | 3 | 1 | no | — |
| 28 | #63944 | D3 | 1 | 1 | yes | characteristic |
| 29 | D3×#216 | — | 6 | 1 | no | — |
| 30 | #63732 | — | 3 | 1 | no | — |
| 31 | #63730 | — | 3 | 1 | no | — |
| 32 | #63730 | — | 3 | 1 | no | — |
| 33 | C2×C3⋊#157 | — | 2 | 1 | no | — |
| 34 | C2×C3⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 36 | C33×Q8 | D4 | 1 | 1 | yes | characteristic |
| 37 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 38 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 39 | C3×#634 | — | 2 | 1 | no | — |
| 40 | C3×#634 | — | 2 | 1 | no | — |
| 41 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 42 | C32×Dic6 | — | 2 | 1 | no | — |
| 43 | #6296 | — | 2 | 1 | no | — |
| 44 | #6294 | — | 2 | 1 | no | — |
| 45 | C3×#627 | — | 2 | 1 | no | — |
| 46 | C3×#624 | — | 2 | 1 | no | — |
| 47 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 48 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 49 | #5182 | — | 9 | 1 | no | maximal |
| 50 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 51 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 52 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 53 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 54 | #3797 | — | 3 | 1 | no | — |
| 55 | #3797 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | D3×Dic6 | — | 6 | 1 | no | — |
| 57 | C4⋊#157 | — | 3 | 1 | no | — |
| 58 | C4⋊#157 | — | 6 | 1 | no | — |
| 59 | C4×#157 | — | 3 | 1 | no | — |
| 60 | C4×#157 | — | 6 | 1 | no | — |
| 61 | #3773 | — | 6 | 1 | no | — |
| 62 | #3773 | — | 6 | 1 | no | — |
| 63 | C32×Q16 | — | 6 | 1 | no | — |
| 64 | #3756 | — | 2 | 1 | no | — |
| 65 | C3×#216 | — | 2 | 1 | no | — |
| 66 | C3×#216 | — | 2 | 1 | no | — |
| 67 | C3×#216 | — | 4 | 1 | no | — |
| 68 | C3×#216 | — | 6 | 1 | no | — |
| 69 | C3×#216 | — | 6 | 1 | no | — |
| 70 | C3×#216 | — | 6 | 1 | no | — |
| 71 | C3×#216 | — | 12 | 1 | no | — |
| 72 | C3×Dic12 | — | 6 | 1 | no | — |
| 73 | C3×D3×C8 | — | 6 | 1 | no | — |
| 74 | #3719 | — | 2 | 1 | no | — |
| 75 | #3719 | — | 6 | 1 | no | — |
| 76 | #3719 | — | 6 | 1 | no | — |
| 77 | #3718 | — | 6 | 1 | no | — |
| 78 | #3710 | — | 3 | 1 | no | — |
| 79 | #3710 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | D3×C3⋊C8 | — | 6 | 1 | no | — |
| 81 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C3⋊#157 | — | 2 | 1 | no | — |
| 83 | C3⋊#157 | — | 4 | 1 | no | — |
| 84 | C3⋊#157 | Q16 | 1 | 2 | yes | complemented |
| 85 | C33×C4 | — | 2 | 1 | no | — |
| 86 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 88 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 89 | C3×C3⋊Dic3 | #41 | 1 | 1 | yes | characteristic |
| 90 | C32×Dic3 | — | 4 | 1 | no | — |
| 91 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 92 | Q8×Dic3 | — | 9 | 1 | no | — |
| 93 | #944 | — | 9 | 1 | no | — |
| 94 | C2×#216 | — | 9 | 1 | no | — |
| 95 | D3×Q16 | — | 6 | 1 | no | — |
| 96 | D3×Q16 | — | 18 | 1 | no | — |
| 97 | #835 | — | 9 | 1 | no | — |
| 98 | #816 | — | 9 | 1 | no | — |
| 99 | Dic3⋊C8 | — | 9 | 1 | no | — |
| 100 | C2×#157 | — | 3 | 1 | no | — |
| 101 | C2×#157 | — | 3 | 1 | no | — |
| 102 | C2×#157 | — | 6 | 1 | no | — |
| 103 | C32×Q8 | — | 2 | 1 | no | — |
| 104 | C32×Q8 | — | 2 | 1 | no | — |
| 105 | C32×Q8 | — | 4 | 1 | no | — |
| 106 | C32×Q8 | — | 4 | 1 | no | — |
| 107 | C32×Q8 | — | 6 | 1 | no | — |
| 108 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 109 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 110 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 111 | #634 | — | 2 | 1 | no | — |
| 112 | #634 | — | 2 | 1 | no | — |
| 113 | #634 | #67 | 1 | 1 | yes | characteristic |
| 114 | C3×C4×D3 | — | 6 | 1 | no | — |
| 115 | C3×C4×D3 | — | 6 | 1 | no | — |
| 116 | C3×C4×D3 | — | 12 | 1 | no | — |
| 117 | C3×C4×D3 | — | 12 | 1 | no | — |
| 118 | C3×C4×D3 | — | 12 | 1 | no | — |
| 119 | C3×Dic6 | — | 2 | 1 | no | — |
| 120 | C3×Dic6 | — | 2 | 1 | no | — |
| 121 | C3×Dic6 | — | 4 | 1 | no | — |
| 122 | C3×Dic6 | — | 6 | 1 | no | — |
| 123 | C3×Dic6 | — | 6 | 1 | no | — |
| 124 | C3×Dic6 | — | 6 | 1 | no | — |
| 125 | C3×Dic6 | — | 6 | 1 | no | — |
| 126 | C3×Dic6 | — | 12 | 1 | no | — |
| 127 | C3×Dic6 | — | 12 | 1 | no | — |
| 128 | C3×Dic6 | — | 12 | 1 | no | — |
| 129 | C3×Dic6 | — | 12 | 1 | no | — |
| 130 | #627 | — | 2 | 1 | no | — |
| 131 | #627 | — | 6 | 1 | no | — |
| 132 | #627 | — | 12 | 1 | no | — |
| 133 | #624 | — | 2 | 1 | no | — |
| 134 | #624 | — | 6 | 1 | no | — |
| 135 | D3×Dic3 | — | 12 | 1 | no | — |
| 136 | C32×C8 | — | 6 | 1 | no | — |
| 137 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 138 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 139 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 140 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 141 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 142 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 143 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 144 | #462 | — | 27 | 1 | no | Sylow |
| 145 | C2×C33 | #121 | 1 | 1 | yes | characteristic |
| 146 | C3×C3⋊D3 | C2×Q16 | 1 | 1 | yes | characteristic |
| 147 | C3×C3⋊D3 | #137 | 1 | 1 | yes | characteristic |
| 148 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 149 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 150 | D3×Q8 | — | 6 | 1 | no | — |
| 151 | D3×Q8 | — | 6 | 1 | no | — |
| 152 | D3×Q8 | — | 6 | 1 | no | — |
| 153 | D3×Q8 | — | 18 | 1 | no | — |
| 154 | C2×Dic6 | — | 9 | 1 | no | — |
| 155 | C3×Q16 | — | 6 | 1 | no | — |
| 156 | C3×Q16 | — | 6 | 1 | no | — |
| 157 | C3×Q16 | — | 12 | 1 | no | — |
| 158 | C3×Q16 | — | 18 | 1 | no | — |
| 159 | C3×Q16 | — | 18 | 1 | no | — |
| 160 | C2×C3×C8 | — | 9 | 1 | no | — |
| 161 | #216 | — | 2 | 1 | no | — |
| 162 | #216 | — | 6 | 1 | no | — |
| 163 | #216 | — | 6 | 1 | no | — |
| 164 | #216 | — | 6 | 1 | no | — |
| 165 | #216 | — | 12 | 1 | no | — |
| 166 | #216 | — | 18 | 1 | no | — |
| 167 | #216 | — | 18 | 1 | no | — |
| 168 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 169 | C4⋊Dic3 | — | 18 | 1 | no | — |
| 170 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 171 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 172 | C4×Dic3 | — | 9 | 1 | no | — |
| 173 | C4×Dic3 | — | 18 | 1 | no | — |
| 174 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 175 | Dic12 | — | 6 | 1 | no | — |
| 176 | Dic12 | — | 18 | 1 | no | — |
| 177 | D3×C8 | — | 6 | 1 | no | — |
| 178 | D3×C8 | — | 18 | 1 | no | — |
| 179 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C3×D3 | — | 6 | 1 | no | — |
| 181 | C2×C3×D3 | — | 6 | 1 | no | — |
| 182 | #157 | — | 3 | 2 | no | — |
| 183 | #157 | — | 6 | 1 | no | — |
| 184 | #157 | — | 12 | 1 | no | — |
| 185 | C32×C4 | — | 2 | 1 | no | — |
| 186 | C32×C4 | — | 2 | 1 | no | — |
| 187 | C32×C4 | — | 2 | 1 | no | — |
| 188 | C32×C4 | — | 4 | 1 | no | — |
| 189 | C32×C4 | — | 4 | 1 | no | — |
| 190 | C32×C4 | — | 4 | 1 | no | — |
| 191 | C32×C4 | — | 4 | 1 | no | — |
| 192 | C32×C4 | — | 8 | 1 | no | — |
| 193 | C32×C4 | — | 8 | 1 | no | — |
| 194 | C32×C4 | — | 12 | 1 | no | — |
| 195 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 196 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 197 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 198 | C3⋊Dic3 | #237 | 1 | 1 | yes | characteristic |
| 199 | C3×Dic3 | — | 4 | 1 | no | — |
| 200 | C3×Dic3 | — | 4 | 1 | no | — |
| 201 | C3×Dic3 | — | 6 | 1 | no | — |
| 202 | C3×Dic3 | — | 6 | 1 | no | — |
| 203 | C3×Dic3 | — | 8 | 1 | no | — |
| 204 | C3×Dic3 | — | 12 | 1 | no | — |
| 205 | C3×Dic3 | — | 12 | 1 | no | — |
| 206 | C3×Dic3 | — | 12 | 1 | no | — |
| 207 | C3×Dic3 | — | 12 | 1 | no | — |
| 208 | C3×Dic3 | — | 24 | 1 | no | — |
| 209 | C2×Q16 | — | 9 | 1 | no | — |
| 210 | C2×Q16 | — | 27 | 1 | no | — |
| 211 | C4⋊Q8 | — | 27 | 1 | no | — |
| 212 | C4×Q8 | — | 27 | 1 | no | — |
| 213 | C4⋊C8 | — | 27 | 1 | no | — |
| 214 | #103 | — | 27 | 1 | no | — |
| 215 | #103 | — | 27 | 1 | no | — |
| 216 | C33 | #462 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 217 | C3×Q8 | — | 2 | 1 | no | — |
| 218 | C3×Q8 | — | 2 | 1 | no | — |
| 219 | C3×Q8 | — | 4 | 1 | no | — |
| 220 | C3×Q8 | — | 4 | 1 | no | — |
| 221 | C3×Q8 | — | 6 | 1 | no | — |
| 222 | C3×Q8 | — | 6 | 1 | no | — |
| 223 | C3×Q8 | — | 9 | 1 | no | — |
| 224 | C3×Q8 | — | 12 | 1 | no | — |
| 225 | C3×Q8 | — | 18 | 1 | no | — |
| 226 | C3×Q8 | — | 18 | 1 | no | — |
| 227 | C3×Q8 | — | 18 | 1 | no | — |
| 228 | C3×Q8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 229 | C2×C3×C4 | — | 9 | 1 | no | — |
| 230 | C2×C3×C4 | — | 18 | 1 | no | — |
| 231 | C2×C3×C4 | — | 18 | 1 | no | — |
| 232 | C2×Dic3 | — | 9 | 1 | no | — |
| 233 | C2×Dic3 | — | 9 | 1 | no | — |
| 234 | C2×Dic3 | — | 18 | 1 | no | — |
| 235 | C2×Dic3 | — | 18 | 1 | no | — |
| 236 | C4×D3 | — | 6 | 1 | no | — |
| 237 | C4×D3 | — | 6 | 1 | no | — |
| 238 | C4×D3 | — | 12 | 1 | no | — |
| 239 | C4×D3 | — | 12 | 1 | no | — |
| 240 | C4×D3 | — | 12 | 1 | no | — |
| 241 | C4×D3 | — | 36 | 1 | no | — |
| 242 | Dic6 | — | 2 | 1 | no | — |
| 243 | Dic6 | — | 6 | 1 | no | — |
| 244 | Dic6 | — | 6 | 1 | no | — |
| 245 | Dic6 | — | 6 | 1 | no | — |
| 246 | Dic6 | — | 6 | 1 | no | — |
| 247 | Dic6 | — | 12 | 1 | no | — |
| 248 | Dic6 | — | 12 | 1 | no | — |
| 249 | Dic6 | — | 12 | 1 | no | — |
| 250 | Dic6 | — | 12 | 1 | no | — |
| 251 | Dic6 | — | 18 | 1 | no | — |
| 252 | Dic6 | — | 36 | 1 | no | — |
| 253 | C3×C8 | — | 6 | 1 | no | — |
| 254 | C3×C8 | — | 6 | 1 | no | — |
| 255 | C3×C8 | — | 12 | 1 | no | — |
| 256 | C3×C8 | — | 18 | 1 | no | — |
| 257 | C3⋊C8 | — | 2 | 1 | no | — |
| 258 | C3⋊C8 | — | 6 | 1 | no | — |
| 259 | C3⋊C8 | — | 6 | 1 | no | — |
| 260 | C3⋊C8 | — | 12 | 1 | no | — |
| 261 | C2×C32 | — | 2 | 1 | no | — |
| 262 | C2×C32 | — | 2 | 1 | no | — |
| 263 | C2×C32 | — | 4 | 1 | no | — |
| 264 | C2×C32 | — | 4 | 1 | no | — |
| 265 | C2×C32 | #939 | 1 | 1 | yes | characteristic |
| 266 | C3⋊D3 | D3×Q16 | 1 | 1 | yes | characteristic |
| 267 | C3⋊D3 | #918 | 1 | 1 | yes | characteristic |
| 268 | C3×D3 | — | 6 | 1 | no | — |
| 269 | C3×D3 | — | 6 | 1 | no | — |
| 270 | C3×D3 | — | 6 | 1 | no | — |
| 271 | C3×D3 | — | 6 | 1 | no | — |
| 272 | C2×Q8 | — | 9 | 1 | no | — |
| 273 | C2×Q8 | — | 9 | 1 | no | — |
| 274 | C2×Q8 | — | 27 | 1 | no | — |
| 275 | Q16 | — | 6 | 1 | no | — |
| 276 | Q16 | — | 18 | 1 | no | — |
| 277 | Q16 | — | 18 | 1 | no | — |
| 278 | Q16 | — | 54 | 1 | no | — |
| 279 | C2×C8 | — | 9 | 1 | no | — |
| 280 | C2×C8 | — | 27 | 1 | no | — |
| 281 | C4⋊C4 | — | 27 | 1 | no | — |
| 282 | C4⋊C4 | — | 54 | 1 | no | — |
| 283 | C4⋊C4 | — | 54 | 1 | no | — |
| 284 | C4⋊C4 | — | 54 | 1 | no | — |
| 285 | C42 | — | 27 | 1 | no | — |
| 286 | C42 | — | 54 | 1 | no | — |
| 287 | C22×C3 | — | 9 | 1 | no | — |
| 288 | C2×D3 | — | 6 | 1 | no | — |
| 289 | C2×D3 | — | 6 | 1 | no | — |
| 290 | C3×C4 | — | 2 | 1 | no | — |
| 291 | C3×C4 | — | 2 | 1 | no | — |
| 292 | C3×C4 | — | 2 | 1 | no | — |
| 293 | C3×C4 | — | 4 | 1 | no | — |
| 294 | C3×C4 | — | 4 | 1 | no | — |
| 295 | C3×C4 | — | 4 | 1 | no | — |
| 296 | C3×C4 | — | 4 | 1 | no | — |
| 297 | C3×C4 | — | 8 | 1 | no | — |
| 298 | C3×C4 | — | 8 | 1 | no | — |
| 299 | C3×C4 | — | 9 | 1 | no | — |
| 300 | C3×C4 | — | 12 | 1 | no | — |
| 301 | C3×C4 | — | 12 | 1 | no | — |
| 302 | C3×C4 | — | 18 | 1 | no | — |
| 303 | C3×C4 | — | 24 | 1 | no | — |
| 304 | C3×C4 | — | 36 | 1 | no | — |
| 305 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 306 | Dic3 | — | 4 | 1 | no | — |
| 307 | Dic3 | — | 6 | 1 | no | — |
| 308 | Dic3 | — | 6 | 1 | no | — |
| 309 | Dic3 | — | 9 | 2 | no | — |
| 310 | Dic3 | — | 12 | 1 | no | — |
| 311 | Dic3 | — | 12 | 1 | no | — |
| 312 | Dic3 | — | 12 | 1 | no | — |
| 313 | Dic3 | — | 12 | 1 | no | — |
| 314 | Dic3 | — | 18 | 1 | no | — |
| 315 | Dic3 | — | 24 | 1 | no | — |
| 316 | Dic3 | — | 36 | 1 | no | — |
| 317 | C32 | — | 2 | 1 | no | — |
| 318 | C32 | — | 2 | 1 | no | — |
| 319 | C32 | — | 4 | 1 | no | — |
| 320 | C32 | — | 4 | 1 | no | — |
| 321 | C32 | #5182 | 1 | 1 | yes | characteristic, complemented |
| 322 | Q8 | — | 6 | 1 | no | — |
| 323 | Q8 | — | 9 | 1 | no | — |
| 324 | Q8 | — | 18 | 1 | no | — |
| 325 | Q8 | — | 18 | 1 | no | — |
| 326 | Q8 | — | 18 | 1 | no | — |
| 327 | Q8 | — | 54 | 1 | no | — |
| 328 | Q8 | D32⋊D3 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | — | 9 | 1 | no | — |
| 330 | C2×C4 | — | 18 | 1 | no | — |
| 331 | C2×C4 | — | 18 | 1 | no | — |
| 332 | C2×C4 | — | 27 | 1 | no | — |
| 333 | C2×C4 | — | 27 | 1 | no | — |
| 334 | C2×C4 | — | 54 | 1 | no | — |
| 335 | C2×C4 | — | 54 | 1 | no | — |
| 336 | C8 | — | 6 | 1 | no | — |
| 337 | C8 | — | 18 | 1 | no | — |
| 338 | C2×C3 | — | 2 | 1 | no | — |
| 339 | C2×C3 | — | 2 | 1 | no | — |
| 340 | C2×C3 | — | 4 | 1 | no | — |
| 341 | C2×C3 | — | 4 | 1 | no | — |
| 342 | C2×C3 | — | 9 | 1 | no | — |
| 343 | C2×C3 | — | 9 | 1 | no | — |
| 344 | C2×C3 | #64242 | 1 | 1 | yes | characteristic |
| 345 | D3 | — | 6 | 1 | no | — |
| 346 | D3 | — | 6 | 1 | no | — |
| 347 | D3 | — | 6 | 1 | no | — |
| 348 | D3 | — | 6 | 1 | no | — |
| 349 | C22 | — | 9 | 1 | no | — |
| 350 | C4 | — | 2 | 1 | no | — |
| 351 | C4 | — | 9 | 1 | no | — |
| 352 | C4 | — | 12 | 1 | no | — |
| 353 | C4 | — | 18 | 1 | no | — |
| 354 | C4 | — | 27 | 2 | no | — |
| 355 | C4 | — | 36 | 1 | no | — |
| 356 | C4 | — | 54 | 1 | no | — |
| 357 | C4 | — | 108 | 1 | no | — |
| 358 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 359 | C3 | — | 2 | 1 | no | — |
| 360 | C3 | — | 2 | 1 | no | — |
| 361 | C3 | — | 4 | 1 | no | — |
| 362 | C3 | — | 4 | 1 | no | — |
| 363 | C3 | #10593477 | 1 | 1 | yes | characteristic, complemented |
| 364 | C2 | — | 9 | 1 | no | — |
| 365 | C2 | — | 9 | 1 | no | — |
| 366 | C2 | #11724332 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 84. C3⋊#157 | Q16 | semidirect |
| 216. C33 | #462 | semidirect |
| 321. C32 | #5182 | semidirect |
| 363. C3 | #10593477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊#157 | 2 |
| #11724302 | 2 |
| #11723710 | 2 |
| C3×#63944 | 2 |
| #11722763 | 2 |
| #11722760 | 2 |
| #11722759 | 2 |
| #10593477 | 3 |
| #5182 | 9 |