Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #11721025 | C2 | semidirect |
| 3. #11720967 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720294 | C2 | semidirect |
| 35. #63376 | D3 | semidirect |
| 223. C3×C9 | #463 | semidirect |
| 320. C9 | #4819 | semidirect |
| 364. C3 | #10588833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| #11721025 | 2 |
| #11720967 | 2 |
| C2×#88423 | 2 |
| #11720537 | 2 |
| C3×#63376 | 2 |
| #11720294 | 2 |
| #10590751 | 3 |
| #10588833 | 3 |