Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
774 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 2. C22×#634 | C2 | semidirect |
| 3. C2×C32×M16 | C2 | semidirect |
| 4. #64118 | C2 | direct (N × H) |
| 5. C2×#3746 | C2 | semidirect |
| 6. C2×#3744 | C2 | semidirect |
| 19. C2×#634 | C22 | semidirect |
| 20. C32×M16 | C22 | semidirect |
| 22. #3746 | C22 | semidirect |
| 23. #3744 | C22 | semidirect |
| 26. C2×C3×M16 | D3 | semidirect |
| 62. C3×M16 | C2×D3 | semidirect |
| 81. C2×M16 | C3⋊D3 | semidirect |
| 102. C2×C32 | #137 | semidirect |
| 119. M16 | C2×C3⋊D3 | semidirect |
| 131. C32 | C2×#137 | semidirect |
| 152. C2×C3 | #909 | semidirect |
| 165. C3 | C2×#909 | semidirect |
| 168. C2 | #64118 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C22×#634 | 2 |
| C2×C32×M16 | 2 |
| #64118 | 2 |
| C2×#3746 | 2 |
| C2×#3744 | 2 |
| C2×#909 | 3 |