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. #64160 | C2 | direct (N × H) |
| 4. C2×#3756 | C2 | semidirect |
| 5. C2×#3754 | C2 | semidirect |
| 6. C2×#3748 | C2 | semidirect |
| 19. C2×#634 | C22 | semidirect |
| 20. #3756 | C22 | semidirect |
| 21. #3754 | C22 | semidirect |
| 22. #3748 | C22 | semidirect |
| 103. C2×C32 | #137 | semidirect |
| 131. C32 | C2×#137 | semidirect |
| 153. C2×C3 | #951 | semidirect |
| 165. C3 | C2×#951 | semidirect |
| 168. C2 | #64160 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41 | 2 |
| C22×#634 | 2 |
| #64160 | 2 |
| C2×#3756 | 2 |
| C2×#3754 | 2 |
| C2×#3748 | 2 |
| C2×#951 | 3 |