Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1114 conjugacy classes of subgroups; only the 445 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 445 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. #10596543 | C2 | semidirect |
| 4. #10596542 | C2 | semidirect |
| 12. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 13. C4×PSU(3,𝔽2) | C22 | semidirect |
| 14. #64243 | C22 | semidirect |
| 18. C22×C32×C4 | Q8 | semidirect |
| 19. C22×C3⋊Dic3 | Q8 | semidirect |
| 20. C2×C4×C3⋊D3 | Q8 | semidirect |
| 21. C2×C4×C3⋊D3 | Q8 | semidirect |
| 104. C22×C4 | PSU(3,𝔽2) | semidirect |
| 120. C32 | #3458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64286 | 2 |
| #10596550 | 2 |
| #10596543 | 2 |
| #10596542 | 2 |
| #3458 | 9 |