Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
432 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 432 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×#3745 | C2 | semidirect |
| 2. C2×#3744 | C2 | semidirect |
| 3. #64084 | C2 | semidirect |
| 4. #64083 | C2 | semidirect |
| 5. C32×#97 | C2 | semidirect |
| 20. C3×#97 | D3 | semidirect |
| 31. C32×C8 | D4 | semidirect |
| 54. #97 | C3⋊D3 | semidirect |
| 65. C3×C8 | D12 | semidirect |
| 87. C32 | #496 | semidirect |
| 98. C8 | C4⋊(C3⋊D3) | semidirect |
| 111. C3 | #4712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745 | 2 |
| C2×#3744 | 2 |
| #64084 | 2 |
| #64083 | 2 |
| C32×#97 | 2 |
| #4712 | 3 |