Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
298 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C3×#815 | C2 | semidirect |
| 5. Dic3×C3⋊C8 | C2 | semidirect |
| 10. C8×C3⋊D3 | C4 | semidirect |
| 15. #3712 | C4 | semidirect |
| 21. #815 | D3 | semidirect |
| 105. C32 | #405 | semidirect |
| 129. C3 | #4708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D3 | 2 |
| #63874 | 2 |
| C2×#3712 | 2 |
| C3×#815 | 2 |
| Dic3×C3⋊C8 | 2 |
| #4708 | 3 |