Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
282 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
| 12. #63765 | C4 | semidirect |
| 14. C2×C32×C16 | C4 | semidirect |
| 15. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 16. C16×C3⋊D3 | C4 | semidirect |
| 17. C16×C3⋊D3 | C4 | semidirect |
| 96. C2×C16 | #157 | semidirect |
| 140. C32 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593765 | 2 |
| #10593762 | 2 |
| C2×C16×C3⋊D3 | 2 |
| #10590135 | 2 |
| C16×#157 | 2 |
| #2108 | 9 |