Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
259 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 259 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 |
|---|---|---|
| 2. C3×#926 | C2 | semidirect |
| 3. C3×#830 | C2 | semidirect |
| 4. #63575 | C2 | semidirect |
| 5. #63573 | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63564 | C2 | semidirect |
| 25. #926 | D3 | semidirect |
| 27. #830 | D3 | semidirect |
| 189. C32 | #482 | semidirect |
| 233. C3 | #4737 | semidirect |
| 234. C3 | #5003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| C3×#926 | 2 |
| C3×#830 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #63564 | 2 |
| #5003 | 3 |
| #4737 | 3 |