Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
433 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 433 conjugacy classes of subgroups — too many to draw. Only its 112 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. C3×C4⋊(C3⋊C8) | C4 | semidirect |
| 14. C3×#803 | C4 | semidirect |
| 56. C4⋊(C3⋊C8) | Dic3 | semidirect |
| 58. #803 | Dic3 | semidirect |
| 224. C32 | #1300 | semidirect |
| 264. C3 | #67665 | semidirect |
| 265. C3 | #67748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592631 | 2 |
| C3×#4926 | 2 |
| C3×C4×#208 | 2 |
| #67748 | 3 |
| #67665 | 3 |