Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 42. #6308 | Q8 | semidirect |
| 44. C32×Dic6 | Q8 | semidirect |
| 45. #6293 | Q8 | semidirect |
| 150. C33 | #557 | semidirect |
| 169. Dic6 | PSU(3,𝔽2) | semidirect |
| 213. C32 | #5721 | semidirect |
| 247. C3 | #10596547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊PSU(3,𝔽2) | 2 |
| #11724362 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| #11724245 | 2 |
| Dic6×#157 | 2 |
| #11724153 | 2 |
| #11724152 | 2 |
| Dic3×PSU(3,𝔽2) | 2 |
| #10596547 | 3 |
| #5721 | 9 |