Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3748 | C2 | semidirect |
| 3. C3×#924 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. #63576 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 28. #924 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 195. C32 | #468 | semidirect |
| 240. C3 | #5042 | semidirect |
| 241. C3 | #5049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3748 | 2 |
| C3×#930 | 2 |
| C3×#924 | 2 |
| C2×#3715 | 2 |
| #63576 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| #5049 | 3 |
| #5042 | 3 |