Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
290 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 72 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. #63860 | C2 | semidirect |
| 4. C2×#3716 | C2 | semidirect |
| 5. C3×C8×Dic3 | C2 | semidirect |
| 27. C8×Dic3 | D3 | semidirect |
| 127. C32 | #495 | semidirect |
| 154. C3 | #4696 | semidirect |
| 155. C3 | #5155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C2×C3×D24 | 2 |
| #63860 | 2 |
| C2×#3716 | 2 |
| C3×C8×Dic3 | 2 |
| #5155 | 3 |
| #4696 | 3 |