Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 201 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. #63630 | C4 | semidirect |
| 15. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 136. C32 | #1747 | semidirect |
| 160. C3 | #68697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592821 | 2 |
| #10592696 | 2 |
| C32×H(3,ℤ/4) | 2 |
| #10589426 | 2 |
| #10589397 | 2 |
| #68697 | 3 |