Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
490 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C4×C9×D12 | C2 | semidirect |
| 4. C3×#63362 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 6. #11720267 | C2 | semidirect |
| 7. #11720264 | C2 | semidirect |
| 21. #88422 | C4 | semidirect |
| 36. #63362 | D3 | semidirect |
| 44. C4⋊(C3⋊D9) | C2×C4 | semidirect |
| 48. C9×D12 | C2×C4 | semidirect |
| 51. C3×C9⋊C8 | C2×C4 | semidirect |
| 102. C4×D12 | D9 | semidirect |
| 148. C9⋊C8 | C4×D3 | semidirect |
| 226. C3×C9 | #442 | semidirect |
| 256. D12 | C4×D9 | semidirect |
| 328. C9 | #4711 | semidirect |
| 372. C3 | #10588697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| C4×C9×D12 | 2 |
| C2×#88422 | 2 |
| C3×#63362 | 2 |
| #11720295 | 2 |
| #11720267 | 2 |
| #11720264 | 2 |
| #10590346 | 3 |
| #10588697 | 3 |