Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
314 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 23. C32×M16 | C8 | semidirect |
| 30. #3748 | C8 | semidirect |
| 121. M16 | #622 | semidirect |
| 144. C32 | #1278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593795 | 2 |
| C2×C4×#622 | 2 |
| M16×C3⋊Dic3 | 2 |
| #1278 | 9 |