Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88638 | C2 | semidirect |
| 2. C2×#88524 | C2 | semidirect |
| 3. #11721004 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. C9×#821 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 7. #11720269 | C2 | semidirect |
| 38. (C2×D9)⋊C8 | D3 | semidirect |
| 48. #6226 | D4 | semidirect |
| 52. C9×D12 | D4 | semidirect |
| 122. #821 | D9 | semidirect |
| 259. C3×C9 | #449 | semidirect |
| 293. D12 | D36 | semidirect |
| 378. C9 | #4734 | semidirect |
| 431. C3 | #10588461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88638 | 2 |
| C2×#88524 | 2 |
| #11721004 | 2 |
| C2×#88422 | 2 |
| C9×#821 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| #11720269 | 2 |
| #10590968 | 3 |
| #10588461 | 3 |