Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
528 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11721711 | C2 | semidirect |
| 2. C4×C9×D12 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720267 | C2 | semidirect |
| 28. C4⋊(C9⋊C8) | D3 | semidirect |
| 40. C9×D12 | D4 | semidirect |
| 77. C3×C4×C9 | D8 | semidirect |
| 87. C4×D12 | D9 | semidirect |
| 187. C4×C9 | D24 | semidirect |
| 195. C3×C9 | #459 | semidirect |
| 228. D12 | D36 | semidirect |
| 281. C3×C4 | #3673 | semidirect |
| 290. C9 | #4843 | semidirect |
| 328. C4 | #88422 | semidirect |
| 332. C3 | #10588698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C4×C9×D12 | 2 |
| C2×#88422 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720267 | 2 |
| #10590349 | 3 |
| #10588698 | 3 |