Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
195 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C9×Q16 | C2 | semidirect |
| 2. #63509 | C2 | semidirect |
| 3. C2×#3675 | C2 | semidirect |
| 5. C8×Dic9 | C2 | semidirect |
| 48. C2×Q16 | D9 | semidirect |
| 82. C9 | #495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Q16 | 2 |
| #63509 | 2 |
| C2×#3675 | 2 |
| C2×D72 | 2 |
| C8×Dic9 | 2 |
| #5191 | 3 |