Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 217 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 | semidirect |
| 11. C2×#3746 | C4 | semidirect |
| 146. C32 | #2141 | semidirect |
| 172. C3 | #70654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C32×#427 | 2 |
| C2×#63639 | 2 |
| #10589358 | 2 |
| #70654 | 3 |