Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 119 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. #10592793 | C2 | semidirect |
| 4. #10592530 | C2 | semidirect |
| 5. C32×#332 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 28. C3×#332 | D3 | semidirect |
| 86. C3⋊(C3⋊C8) | SD16 | semidirect |
| 92. #332 | C3⋊D3 | semidirect |
| 196. C32 | #1686 | semidirect |
| 234. C3 | #68472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592793 | 2 |
| #10592784 | 2 |
| #10592547 | 2 |
| #10592530 | 2 |
| C32×#332 | 2 |
| #10589351 | 2 |
| #10589345 | 2 |
| #68472 | 3 |