Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #10590089 | C2 | semidirect |
| 39. #622 | M16 | semidirect |
| 107. C32 | #1567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593805 | 2 |
| C2×C4×#622 | 2 |
| #10590089 | 2 |
| #1567 | 9 |