Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 177 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 | direct (N × H) |
| 56. C32×C8 | Q16 | semidirect |
| 104. C3×C8 | Dic12 | semidirect |
| 129. C32 | C8×Q16 | semidirect |
| 142. C8 | #3746 | direct (N × H) |
| 154. C3 | C8×Dic12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C8×#634 | 2 |
| C32×C82 | 2 |
| #10589324 | 2 |
| #10589322 | 2 |
| C8×Dic12 | 3 |