Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 466 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×#88525 | C2 | semidirect |
| 2. C2×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #11721038 | C2 | semidirect |
| 4. C3×#63377 | C2 | semidirect |
| 5. #11720284 | C2 | semidirect |
| 27. #63377 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 78. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 112. C8×C9 | D12 | semidirect |
| 170. C3×C9 | #469 | semidirect |
| 197. C3×C8 | #611 | semidirect |
| 248. C9 | #4865 | semidirect |
| 260. C8 | #6195 | semidirect |
| 283. C3 | #10588817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| #11721038 | 2 |
| C3×#63377 | 2 |
| #11720284 | 2 |
| #10590835 | 3 |
| #10588817 | 3 |