Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 410 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. C4×C9×D12 | C2 | semidirect |
| 2. C3×#63437 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 5. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 33. #63437 | D3 | semidirect |
| 105. C4×D12 | D9 | semidirect |
| 223. C3×C9 | #463 | semidirect |
| 320. C9 | #5057 | semidirect |
| 364. C3 | #10588699 | 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×#63437 | 2 |
| C2×#88423 | 2 |
| C2×#88421 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720268 | 2 |
| #11720266 | 2 |
| #10590348 | 3 |
| #10588699 | 3 |