Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
254 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 62 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×#3746 | C2 | semidirect |
| 3. #63844 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. #63567 | C2 | semidirect |
| 36. Dic3⋊C8 | D3 | semidirect |
| 184. C32 | #464 | semidirect |
| 223. C3 | #4767 | semidirect |
| 224. C3 | #4845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| #63860 | 2 |
| #63844 | 2 |
| C2×#3716 | 2 |
| C3×#821 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63567 | 2 |
| #4845 | 3 |
| #4767 | 3 |