Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11724344 | C2 | semidirect |
| 2. #11724336 | C2 | semidirect |
| 3. #11723647 | C2 | semidirect |
| 4. C3×C8×#157 | C2 | semidirect |
| 18. C8×#157 | D3 | semidirect |
| 25. C3×#622 | D4 | semidirect |
| 26. C33×C8 | D4 | semidirect |
| 27. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 46. C3×#157 | D8 | semidirect |
| 66. #622 | D12 | semidirect |
| 69. C32×C8 | D12 | semidirect |
| 70. C3⋊(C3⋊C8) | D12 | semidirect |
| 98. #157 | D24 | semidirect |
| 108. C33 | #493 | semidirect |
| 125. C3×C8 | GO+(4,𝔽2) | semidirect |
| 160. C32 | #4695 | semidirect |
| 169. C8 | #157⋊D3 | semidirect |
| 187. C3 | #10593293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724344 | 2 |
| #11724336 | 2 |
| #11723647 | 2 |
| C3×C8×#157 | 2 |
| #10593293 | 3 |
| #4695 | 9 |