Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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×C4⋊Q8 | C2 | semidirect |
| 4. #63366 | C2 | semidirect |
| 5. C4⋊(C9⋊C8) | C2 | semidirect |
| 29. D36 | Q8 | semidirect |
| 52. C4⋊Q8 | D9 | semidirect |
| 91. C9 | #474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C4⋊Q8 | 2 |
| C4×D36 | 2 |
| #63369 | 2 |
| #63366 | 2 |
| C4⋊(C9⋊C8) | 2 |
| #5087 | 3 |