Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 95 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×#893 | C2 | semidirect |
| 2. #11721006 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C3×#63369 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 36. #63369 | D3 | semidirect |
| 48. C9×D12 | D4 | semidirect |
| 101. C9×Dic3 | D8 | semidirect |
| 108. #893 | D9 | semidirect |
| 239. C3×C9 | #459 | semidirect |
| 275. D12 | D36 | semidirect |
| 347. Dic3 | #3673 | semidirect |
| 350. C9 | #4786 | semidirect |
| 401. C3 | #10588698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#893 | 2 |
| #11721006 | 2 |
| C2×#88422 | 2 |
| C2×#88421 | 2 |
| #11720528 | 2 |
| C3×#63369 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590547 | 3 |
| #10588698 | 3 |