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×C3×D72 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 4. #11720233 | C2 | semidirect |
| 5. #11720232 | C2 | semidirect |
| 11. #88525 | C22 | semidirect |
| 13. #88521 | C22 | semidirect |
| 16. C9×C3⋊C16 | C22 | semidirect |
| 24. C2×D72 | D3 | semidirect |
| 78. #812 | D9 | semidirect |
| 135. C3⋊C16 | C2×D9 | semidirect |
| 160. C3×C9 | #509 | semidirect |
| 229. C9 | #5147 | semidirect |
| 259. C3 | #10588588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C2×C3×D72 | 2 |
| C9×#812 | 2 |
| #11720233 | 2 |
| #11720232 | 2 |
| #10590633 | 3 |
| #10588588 | 3 |