Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 1. C3×#64078 | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 4. #11722053 | C2 | semidirect |
| 18. #64078 | D3 | semidirect |
| 36. C32×D12 | Q8 | semidirect |
| 102. C3×D12 | Dic6 | semidirect |
| 163. C33 | #476 | semidirect |
| 184. D12 | #634 | semidirect |
| 236. C32 | #5008 | semidirect |
| 237. C32 | #5084 | semidirect |
| 271. C3 | #10590266 | semidirect |
| 272. C3 | #10592707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×C4×D12 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722053 | 2 |
| #11722031 | 2 |
| #10592707 | 3 |
| #10590266 | 3 |