Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
286 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. #10590135 | C2 | semidirect |
| 5. C16×#157 | C2 | semidirect |
| 9. #63773 | C4 | semidirect |
| 14. #63765 | C4 | semidirect |
| 16. C32×M32 | C4 | semidirect |
| 17. #63639 | C4 | semidirect |
| 18. #63625 | C4 | semidirect |
| 36. #3708 | C2×C4 | semidirect |
| 37. C32×C16 | C2×C4 | semidirect |
| 38. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 80. #157 | M32 | direct (N × H) |
| 92. M32 | #157 | direct (N × H) |
| 131. C16 | C2×#157 | semidirect |
| 140. C32 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#157 | 2 |
| #10593762 | 2 |
| C3⋊D3×M32 | 2 |
| #10590135 | 2 |
| C16×#157 | 2 |
| C4×M32 | 9 |