Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 63 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. Q16×C3⋊D3 | C2 | semidirect |
| 3. C32×SD32 | C2 | semidirect |
| 4. #63656 | C2 | semidirect |
| 5. #63654 | C2 | semidirect |
| 6. #63628 | C2 | semidirect |
| 7. #63625 | C2 | semidirect |
| 22. C3×SD32 | D3 | semidirect |
| 62. SD32 | C3⋊D3 | semidirect |
| 96. C32 | #510 | semidirect |
| 118. C3 | #4915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C3⋊D3 | 2 |
| #64121 | 2 |
| C32×SD32 | 2 |
| #63656 | 2 |
| #63654 | 2 |
| #63628 | 2 |
| #63625 | 2 |
| #4915 | 3 |