Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 1. #11721836 | C2 | semidirect |
| 3. #11721025 | C2 | semidirect |
| 4. C2×#88424 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720277 | C2 | semidirect |
| 7. #11720273 | C2 | semidirect |
| 35. #63392 | D3 | semidirect |
| 235. C3×C9 | #463 | semidirect |
| 341. C9 | #4787 | semidirect |
| 386. C3 | #10588833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721836 | 2 |
| C2×C9×#213 | 2 |
| #11721025 | 2 |
| C2×#88424 | 2 |
| C3×#63392 | 2 |
| #11720277 | 2 |
| #11720273 | 2 |
| #10591434 | 3 |
| #10588833 | 3 |