Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
780 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 16. #64079 | C4 | semidirect |
| 180. C32 | #1989 | semidirect |
| 218. C3 | #70461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64079 | 2 |
| C2×C32×C4⋊C8 | 2 |
| C4×C4⋊(C3⋊Dic3) | 2 |
| #10589417 | 2 |
| #70461 | 3 |