Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#88524 | C2 | semidirect |
| 2. C2×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #11720961 | C2 | semidirect |
| 5. C3×#63378 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 36. #63378 | D3 | semidirect |
| 52. C3×C8×C9 | D4 | semidirect |
| 105. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 153. C8×C9 | D12 | semidirect |
| 230. C3×C9 | #468 | semidirect |
| 268. C3×C8 | #611 | semidirect |
| 333. C9 | #4886 | semidirect |
| 349. C8 | #6195 | semidirect |
| 378. C3 | #10588816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| #11721038 | 2 |
| #11720961 | 2 |
| C3×#63378 | 2 |
| #11720284 | 2 |
| #11720277 | 2 |
| #10590838 | 3 |
| #10588816 | 3 |