Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 350 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. C9×#907 | C2 | semidirect |
| 2. #11720891 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. #11720556 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720280 | C2 | semidirect |
| 36. #63383 | D3 | semidirect |
| 105. #907 | D9 | semidirect |
| 217. C3×C9 | #471 | semidirect |
| 303. C9 | #4748 | semidirect |
| 339. C3 | #10588822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#907 | 2 |
| #11720891 | 2 |
| #11720882 | 2 |
| C2×#88415 | 2 |
| #11720556 | 2 |
| C3×#63383 | 2 |
| #11720280 | 2 |
| #10590996 | 3 |
| #10588822 | 3 |