Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
764 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 32. C33×C8 | Q8 | semidirect |
| 33. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 87. C32×C8 | Dic6 | semidirect |
| 88. C32×C8 | Dic6 | semidirect |
| 137. C33 | #500 | semidirect |
| 154. C3×C8 | #627 | semidirect |
| 155. C3×C8 | #634 | semidirect |
| 195. C32 | #4874 | semidirect |
| 196. C32 | #4874 | semidirect |
| 204. C8 | #6293 | semidirect |
| 222. C3 | #10590902 | semidirect |
| 223. C3 | #10592573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723536 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C3×#63645 | 2 |
| C32×#818 | 2 |
| #11722056 | 2 |
| #10592573 | 3 |
| #10590902 | 3 |