Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
790 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 3. #10593774 | C2 | semidirect |
| 4. #10593768 | C2 | semidirect |
| 13. C2×C32×M16 | C4 | semidirect |
| 14. C2×#3748 | C4 | semidirect |
| 15. M16×C3⋊D3 | C4 | semidirect |
| 17. C2×#3743 | C4 | semidirect |
| 19. #63769 | C22 | semidirect |
| 20. #63768 | C22 | semidirect |
| 40. C32×M16 | C2×C4 | semidirect |
| 41. C2×C32×C8 | C2×C4 | semidirect |
| 42. #3748 | C2×C4 | semidirect |
| 43. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 44. #3743 | C2×C4 | semidirect |
| 45. C8×C3⋊D3 | C2×C4 | semidirect |
| 127. C2×M16 | #157 | semidirect |
| 184. M16 | C2×#157 | semidirect |
| 188. C2×C8 | C2×#157 | semidirect |
| 211. C32 | #2911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64286 | 2 |
| C2×M16×C3⋊D3 | 2 |
| #10593774 | 2 |
| #10593768 | 2 |
| #2911 | 9 |