Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 170 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. #11723494 | C2 | semidirect |
| 2. D12×C3⋊Dic3 | C2 | semidirect |
| 4. #11722191 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. C32×#821 | C2 | semidirect |
| 7. #11722057 | C2 | semidirect |
| 21. #88790 | C4 | semidirect |
| 32. C8×C3⋊Dic3 | D3 | semidirect |
| 34. C3×#821 | D3 | semidirect |
| 42. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 47. C32×D12 | C2×C4 | semidirect |
| 51. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 92. C3×C3⋊Dic3 | D8 | semidirect |
| 105. #821 | C3⋊D3 | semidirect |
| 137. C3×D12 | C4×D3 | semidirect |
| 143. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 207. C3⋊Dic3 | D24 | semidirect |
| 218. C33 | C4×D8 | semidirect |
| 246. D12 | C4×C3⋊D3 | semidirect |
| 315. C32 | C4×D24 | semidirect |
| 316. C32 | #4756 | semidirect |
| 360. C3 | #10590745 | semidirect |
| 361. C3 | #10592455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723494 | 2 |
| D12×C3⋊Dic3 | 2 |
| C2×#88790 | 2 |
| #11722191 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C32×#821 | 2 |
| #11722057 | 2 |
| #10592455 | 3 |
| #10590745 | 3 |