Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1474 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 1474 conjugacy classes of subgroups — too many to draw. Only its 384 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3×#3718 | C2 | direct (N × H) |
| 5. C22×#3718 | C3 | direct (N × H) |
| 11. C3×#3718 | C22 | direct (N × H) |
| 20. C2×#3718 | C2×C3 | direct (N × H) |
| 51. #3718 | C22×C3 | direct (N × H) |
| 52. C22×C33 | Q16 | semidirect |
| 97. C2×C33 | C2×Q16 | semidirect |
| 127. C22×C32 | #216 | semidirect |
| 128. C22×C32 | C3×Q16 | semidirect |
| 148. C33 | C22×Q16 | semidirect |
| 185. C2×C32 | C2×#216 | semidirect |
| 186. C2×C32 | C2×C3×Q16 | semidirect |
| 201. C22×C3 | #3718 | direct (N × H) |
| 202. C22×C3 | C3×#216 | semidirect |
| 222. C32 | C22×#216 | semidirect |
| 223. C32 | C22×C3×Q16 | semidirect |
| 237. C2×C3 | C2×#3718 | direct (N × H) |
| 238. C2×C3 | C2×C3×#216 | semidirect |
| 241. C22 | C3×#3718 | direct (N × H) |
| 249. C3 | C22×#3718 | direct (N × H) |
| 250. C3 | C22×C3×#216 | semidirect |
| 251. C2 | C2×C3×#3718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic6 | 2 |
| C22×C3×C3⋊(C3⋊C8) | 2 |
| C2×C3×#3718 | 2 |
| C22×C3×#216 | 3 |
| C22×#3718 | 3 |