Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
744 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 179 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. #64364 | C2 | semidirect |
| 2. C2×C32×Q16 | C2 | semidirect |
| 3. #64151 | C2 | semidirect |
| 4. #64128 | C2 | semidirect |
| 5. #64127 | C2 | semidirect |
| 6. Q16×C3⋊D3 | C2 | semidirect |
| 7. #64113 | C2 | semidirect |
| 8. #64110 | C2 | semidirect |
| 30. C2×C3×Q16 | D3 | semidirect |
| 90. C2×Q16 | C3⋊D3 | semidirect |
| 142. C32 | #578 | semidirect |
| 174. C3 | #5766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64364 | 2 |
| C2×C32×Q16 | 2 |
| #64151 | 2 |
| #64128 | 2 |
| #64127 | 2 |
| Q16×C3⋊D3 | 2 |
| #64113 | 2 |
| #64110 | 2 |
| #5766 | 3 |