Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
354 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 4. #10593165 | C2 | semidirect |
| 6. C22×PSU(3,𝔽2) | C4 | semidirect |
| 11. C22⋊PSU(3,𝔽2) | C4 | semidirect |
| 14. C2×#3777 | C4 | semidirect |
| 190. C32 | #1520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊PSU(3,𝔽2) | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| #10593516 | 2 |
| #10593165 | 2 |
| #1520 | 9 |