Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
721 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 721 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|---|
| 10. C3×C4×C3⋊C8 | C4 | semidirect |
| 23. C4×C3⋊Dic3 | C8 | semidirect |
| 38. C4×C3⋊C8 | Dic3 | semidirect |
| 142. C32 | #1744 | semidirect |
| 171. C3 | #69750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊Dic3 | 2 |
| C2×C3×C4×C3⋊C8 | 2 |
| #10589156 | 2 |
| #69750 | 3 |