Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
834 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 1. C32×#543 | C2 | semidirect |
| 3. #10589393 | C2 | semidirect |
| 10. C3×#543 | D3 | semidirect |
| 14. C23×C3⋊D3 | Q8 | semidirect |
| 20. C22×C3⋊Dic3 | Q8 | semidirect |
| 46. #543 | C3⋊D3 | semidirect |
| 121. C32 | #2032 | semidirect |
| 152. C3 | #71896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#543 | 2 |
| C2×#63633 | 2 |
| #10589393 | 2 |
| #71896 | 3 |