Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 342 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. #64145 | C2 | semidirect |
| 3. #63831 | C2 | semidirect |
| 4. C3×#833 | C2 | semidirect |
| 5. #63568 | C2 | semidirect |
| 9. C2×#634 | C22 | semidirect |
| 15. C4×C3⋊Dic3 | C22 | semidirect |
| 16. C3×#208 | C22 | semidirect |
| 28. #833 | D3 | semidirect |
| 68. #208 | C2×D3 | semidirect |
| 158. C32 | #455 | semidirect |
| 194. C3 | #4746 | semidirect |
| 195. C3 | #5242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1004 | 2 |
| #64145 | 2 |
| #63831 | 2 |
| C3×#833 | 2 |
| #63568 | 2 |
| #5242 | 3 |
| #4746 | 3 |