Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C3×C9×D16 | C2 | semidirect |
| 2. #11720507 | C2 | semidirect |
| 3. C3⋊(C9⋊C32) | C2 | semidirect |
| 12. C9×D16 | D3 | semidirect |
| 29. C3×D16 | D9 | semidirect |
| 58. D16 | C3⋊D9 | semidirect |
| 60. C3×C9 | D32 | semidirect |
| 83. C9 | #4519 | semidirect |
| 96. C3 | #10588196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×D16 | 2 |
| #11720507 | 2 |
| C3⋊(C9⋊C32) | 2 |
| #10589385 | 3 |
| #10588196 | 3 |