Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
634 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 192 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×C3×Dic6 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C2×#3715 | C2 | direct (N × H) |
| 13. C2×C3×Dic6 | C22 | semidirect |
| 14. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. #3715 | C22 | direct (N × H) |
| 19. C22×Dic6 | D3 | semidirect |
| 34. C3×Dic6 | C23 | semidirect |
| 35. C3⋊(C3⋊C8) | C23 | semidirect |
| 51. C2×Dic6 | C2×D3 | semidirect |
| 57. C22×C32 | SD16 | semidirect |
| 90. Dic6 | C22×D3 | semidirect |
| 94. C2×C32 | C2×SD16 | semidirect |
| 110. C22×C3 | #214 | semidirect |
| 111. C22×C3 | #215 | semidirect |
| 124. C32 | C22×SD16 | semidirect |
| 139. C2×C3 | C2×#214 | semidirect |
| 140. C2×C3 | C2×#215 | semidirect |
| 146. C22 | #3715 | direct (N × H) |
| 152. C3 | C22×#214 | semidirect |
| 153. C3 | C22×#215 | semidirect |
| 155. C2 | C2×#3715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C22×C3×Dic6 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| C2×#3715 | 2 |
| C22×#215 | 3 |
| C22×#214 | 3 |