Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
250 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 64 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. #64135 | C2 | semidirect |
| 3. C3×#830 | C2 | semidirect |
| 4. #63575 | C2 | semidirect |
| 5. #63573 | C2 | semidirect |
| 6. #63563 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 29. #830 | D3 | semidirect |
| 184. C32 | #482 | semidirect |
| 227. C3 | #4737 | semidirect |
| 228. C3 | #5035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64135 | 2 |
| C3×#930 | 2 |
| C3×#830 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #63563 | 2 |
| #5035 | 3 |
| #4737 | 3 |