Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#88547 | C2 | semidirect |
| 5. C3×C9×#101 | C2 | semidirect |
| 6. #11720556 | C2 | semidirect |
| 7. #11720555 | C2 | semidirect |
| 36. C9×#101 | D3 | semidirect |
| 102. C3×#101 | D9 | semidirect |
| 194. #101 | C3⋊D9 | semidirect |
| 195. C3×C9 | #473 | semidirect |
| 264. C9 | #4755 | semidirect |
| 294. C3 | #10588435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721853 | 2 |
| C2×#88547 | 2 |
| #11721784 | 2 |
| #11721782 | 2 |
| C3×C9×#101 | 2 |
| #11720556 | 2 |
| #11720555 | 2 |
| #10592454 | 3 |
| #10588435 | 3 |