Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
232 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 12. C32×Q32 | C4 | semidirect |
| 13. #63656 | C4 | semidirect |
| 14. #63628 | C4 | semidirect |
| 62. #157 | Q32 | direct (N × H) |
| 71. Q32 | #157 | direct (N × H) |
| 105. C32 | C4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#157 | 2 |
| C3⋊D3×Q32 | 2 |
| #10590197 | 2 |
| #10590138 | 2 |
| C16×#157 | 2 |
| C4×Q32 | 9 |