Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
930 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #10596216 | C2 | semidirect |
| 3. #10592838 | C2 | semidirect |
| 4. #10592812 | C2 | semidirect |
| 5. #10592809 | C2 | semidirect |
| 6. C32×#341 | C2 | semidirect |
| 7. #10589425 | C2 | semidirect |
| 17. #64118 | C4 | semidirect |
| 19. #64117 | C4 | semidirect |
| 33. C3×#341 | D3 | semidirect |
| 131. #341 | C3⋊D3 | semidirect |
| 295. C32 | #1881 | semidirect |
| 349. C3 | #68947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596219 | 2 |
| #10596216 | 2 |
| #10592838 | 2 |
| #10592812 | 2 |
| #10592809 | 2 |
| C32×#341 | 2 |
| #10589425 | 2 |
| #68947 | 3 |