Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 33. #3746 | C8 | semidirect |
| 57. C3⋊(C3⋊C8) | Q16 | semidirect |
| 129. C32 | C8×Q16 | semidirect |
| 154. C3 | #68557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592529 | 2 |
| C4×#3746 | 2 |
| C32×#335 | 2 |
| #10589350 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #68557 | 3 |