Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
486 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 99 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×#3830 | C2 | semidirect |
| 2. C2×C32×D8 | C2 | semidirect |
| 3. #64147 | C2 | semidirect |
| 4. C2×#3754 | C2 | semidirect |
| 5. #63659 | C2 | semidirect |
| 6. #63647 | C2 | semidirect |
| 7. #63643 | C2 | semidirect |
| 25. C2×C3×D8 | D3 | semidirect |
| 37. C32×D4 | D4 | semidirect |
| 48. #634 | D4 | semidirect |
| 84. C2×D8 | C3⋊D3 | semidirect |
| 95. C3×D4 | #67 | semidirect |
| 145. C32 | #449 | semidirect |
| 156. D4 | #638 | semidirect |
| 187. C3 | #5158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3830 | 2 |
| C2×C32×D8 | 2 |
| #64147 | 2 |
| C2×#3754 | 2 |
| #63659 | 2 |
| #63647 | 2 |
| #63643 | 2 |
| #5158 | 3 |