Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 465 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 |
|---|---|---|
| 12. #63642 | C4 | semidirect |
| 13. C8×C3⋊Dic3 | C4 | semidirect |
| 14. C3×#815 | C4 | semidirect |
| 15. C3×C8×Dic3 | C4 | semidirect |
| 55. #815 | Dic3 | semidirect |
| 58. C8×Dic3 | Dic3 | semidirect |
| 192. C32 | #1747 | semidirect |
| 221. C3 | #69895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592800 | 2 |
| C3×#5101 | 2 |
| #10589159 | 2 |
| #10589158 | 2 |
| #10589157 | 2 |
| #69895 | 3 |