Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 436 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×C9×D12 | C2 | semidirect |
| 2. C3×C4×D36 | C2 | semidirect |
| 4. #11720516 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720266 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 21. #88421 | C4 | semidirect |
| 31. C4×D36 | D3 | semidirect |
| 45. C9×D12 | C2×C4 | semidirect |
| 48. C3×D36 | C2×C4 | semidirect |
| 51. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 99. C4×D12 | D9 | semidirect |
| 138. D36 | C4×D3 | semidirect |
| 215. C3×C9 | #442 | semidirect |
| 242. D12 | C4×D9 | semidirect |
| 309. C9 | #5014 | semidirect |
| 352. C3 | #10588697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×D12 | 2 |
| C3×C4×D36 | 2 |
| C2×#88421 | 2 |
| #11720516 | 2 |
| #11720294 | 2 |
| #11720266 | 2 |
| #11720265 | 2 |
| #10590344 | 3 |
| #10588697 | 3 |