Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 131 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×#88525 | C2 | semidirect |
| 3. C3×C9×M32 | C2 | semidirect |
| 4. #11720508 | C2 | semidirect |
| 5. #11720507 | C2 | semidirect |
| 13. #88525 | C22 | semidirect |
| 15. #88521 | C22 | semidirect |
| 16. C3×C9×C16 | C22 | semidirect |
| 24. C9×M32 | D3 | semidirect |
| 56. C9×C16 | C2×D3 | semidirect |
| 68. C3×M32 | D9 | semidirect |
| 115. C3×C16 | C2×D9 | semidirect |
| 135. M32 | C3⋊D9 | semidirect |
| 136. C3×C9 | #509 | semidirect |
| 173. C16 | C2×C3⋊D9 | semidirect |
| 189. C9 | #4908 | semidirect |
| 215. 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×#88525 | 2 |
| C3×C9×M32 | 2 |
| #11720508 | 2 |
| #11720507 | 2 |
| #10592607 | 3 |
| #10588588 | 3 |