Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
332 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11721773 | C2 | semidirect |
| 2. C2×C9×D24 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 4. #11720241 | C2 | semidirect |
| 5. #11720239 | C2 | semidirect |
| 11. #88525 | C22 | semidirect |
| 13. #88521 | C22 | semidirect |
| 16. C3×C9⋊C16 | C22 | semidirect |
| 27. #63371 | D3 | semidirect |
| 62. C9⋊C16 | C2×D3 | semidirect |
| 74. C2×D24 | D9 | semidirect |
| 160. C3×C9 | #509 | semidirect |
| 229. C9 | #4908 | semidirect |
| 259. C3 | #10588827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C2×C9×D24 | 2 |
| C3×#63371 | 2 |
| #11720241 | 2 |
| #11720239 | 2 |
| #10590633 | 3 |
| #10588827 | 3 |