Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 410 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. Q16×C3⋊D9 | C2 | semidirect |
| 3. C3×C9×SD32 | C2 | semidirect |
| 4. #11720568 | C2 | semidirect |
| 5. #11720564 | C2 | semidirect |
| 6. #11720509 | C2 | semidirect |
| 7. #11720506 | C2 | semidirect |
| 30. C9×SD32 | D3 | semidirect |
| 81. C3×SD32 | D9 | semidirect |
| 158. SD32 | C3⋊D9 | semidirect |
| 160. C3×C9 | #510 | semidirect |
| 215. C9 | #4915 | semidirect |
| 240. C3 | #10588595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C3⋊D9 | 2 |
| #11721791 | 2 |
| C3×C9×SD32 | 2 |
| #11720568 | 2 |
| #11720564 | 2 |
| #11720509 | 2 |
| #11720506 | 2 |
| #10592614 | 3 |
| #10588595 | 3 |