Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 3. #10589106 | C2 | semidirect |
| 10. C3×#812 | C4 | semidirect |
| 12. C2×C3×C3⋊C16 | C4 | semidirect |
| 43. #812 | Dic3 | semidirect |
| 45. C2×C3⋊C16 | Dic3 | semidirect |
| 152. C32 | #2110 | semidirect |
| 178. C3 | #71425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592800 | 2 |
| C2×C3×#812 | 2 |
| #10589106 | 2 |
| #71425 | 3 |