Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
696 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 265 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 |
|---|---|---|
| 4. #10589358 | C2 | direct (N × H) |
| 11. C2×#3746 | C4 | semidirect |
| 36. #3746 | C2×C4 | semidirect |
| 121. C2×C32 | #358 | semidirect |
| 151. C32 | C2×#358 | semidirect |
| 167. C2×C3 | #4492 | semidirect |
| 180. C3 | C2×#4492 | semidirect |
| 181. C2 | #10589358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C2×C32×#107 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| #10589358 | 2 |
| C2×#4492 | 3 |