Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 58. #6308 | Q8 | semidirect |
| 60. C32×Dic6 | Q8 | semidirect |
| 61. #6293 | Q8 | semidirect |
| 195. C33 | #557 | semidirect |
| 217. Dic6 | PSU(3,𝔽2) | semidirect |
| 271. C32 | #5685 | semidirect |
| 311. C3 | #10596547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724364 | 2 |
| C4×C3⋊PSU(3,𝔽2) | 2 |
| #11724362 | 2 |
| C3×#64243 | 2 |
| #11724245 | 2 |
| Dic6×#157 | 2 |
| #11724154 | 2 |
| #11724152 | 2 |
| #11724148 | 2 |
| #10596547 | 3 |
| #5685 | 9 |