Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
641 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 641 conjugacy classes of subgroups — too many to draw. Only its 146 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. C32×#493 | C2 | semidirect |
| 2. C3×#5073 | C2 | semidirect |
| 3. C3×#4695 | C2 | semidirect |
| 4. C3×C8×C3⋊C8 | C2 | semidirect |
| 6. #71276 | C3 | direct (N × H) |
| 17. C3×#493 | D3 | semidirect |
| 18. C3×#493 | C2×C3 | semidirect |
| 19. #5073 | C2×C3 | semidirect |
| 20. #4695 | C2×C3 | semidirect |
| 22. C8×C3⋊C8 | C2×C3 | semidirect |
| 59. C32×C8 | D8 | semidirect |
| 60. C3×C3⋊C8 | D8 | semidirect |
| 63. #493 | C3×D3 | semidirect |
| 127. C3×C8 | #213 | semidirect |
| 128. C3×C8 | C3×D8 | semidirect |
| 129. C3⋊C8 | C3×D8 | semidirect |
| 163. C32 | #1712 | semidirect |
| 173. C8 | C3×#213 | semidirect |
| 193. C3 | #71276 | direct (N × H) |
| 194. C3 | C3×#1712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5073 | 2 |
| C3×#4695 | 2 |
| C3×C8×C3⋊C8 | 2 |
| C3×#1712 | 3 |
| #71276 | 3 |