Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
702 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 138 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×Dic3×D12 | C2 | semidirect |
| 3. #11722080 | C2 | semidirect |
| 4. #11722031 | C2 | semidirect |
| 5. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 15. C3×#3713 | C4 | semidirect |
| 19. Dic3×D12 | D3 | semidirect |
| 36. C32×D12 | C2×C4 | semidirect |
| 39. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 68. #3713 | Dic3 | direct (N × H) |
| 77. C32×Dic3 | D8 | semidirect |
| 118. C3×D12 | C4×D3 | semidirect |
| 119. C3×D12 | C2×Dic3 | semidirect |
| 127. C3⋊(C3⋊C8) | C2×Dic3 | semidirect |
| 198. C3×Dic3 | #213 | semidirect |
| 204. C33 | C4×D8 | semidirect |
| 233. D12 | D3×Dic3 | semidirect |
| 306. Dic3 | #3713 | direct (N × H) |
| 310. C32 | C4×#213 | semidirect |
| 311. C32 | Dic3×D8 | semidirect |
| 353. C3 | C4×#3713 | semidirect |
| 354. C3 | Dic3×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×D12 | 2 |
| C2×C3×#3713 | 2 |
| #11722080 | 2 |
| #11722031 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| Dic3×#213 | 3 |
| C4×#3713 | 3 |