Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
250 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
| 4. C3×#817 | C2 | semidirect |
| 5. #63567 | C2 | semidirect |
| 25. #817 | D3 | semidirect |
| 133. C32 | #470 | semidirect |
| 162. C3 | #4867 | semidirect |
| 163. C3 | #5137 | 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×ΓL(1,𝔽25) | 2 |
| #63857 | 2 |
| C3×#817 | 2 |
| #63567 | 2 |
| #5137 | 3 |
| #4867 | 3 |