Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2268 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 565 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. C32×#568 | C2 | semidirect |
| 3. #10596290 | C2 | semidirect |
| 4. #10592831 | C2 | semidirect |
| 5. C2×#63650 | C2 | semidirect |
| 15. C2×C32×M16 | C22 | semidirect |
| 17. C2×#3748 | C22 | semidirect |
| 18. #63651 | C22 | semidirect |
| 19. #63650 | C22 | semidirect |
| 21. C3×#568 | D3 | semidirect |
| 57. C2×C3×M16 | C2×D3 | semidirect |
| 84. #568 | C3⋊D3 | semidirect |
| 130. C2×M16 | C2×C3⋊D3 | semidirect |
| 190. C32 | #2888 | semidirect |
| 225. C3 | #83813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64366 | 2 |
| C32×#568 | 2 |
| #10596290 | 2 |
| #10592831 | 2 |
| C2×#63650 | 2 |
| #83813 | 3 |