Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#3744 | C2 | semidirect |
| 4. #64084 | C2 | semidirect |
| 5. C32×C4×C8 | C2 | semidirect |
| 20. C3×C4×C8 | D3 | semidirect |
| 52. C4×C8 | C3⋊D3 | semidirect |
| 82. C32 | #495 | semidirect |
| 103. C3 | #4696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C2×#3745 | 2 |
| C2×#3744 | 2 |
| #64084 | 2 |
| C32×C4×C8 | 2 |
| #4696 | 3 |