Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
520 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 5. #10593555 | C2 | semidirect |
| 6. #10593267 | C2 | semidirect |
| 7. #10593166 | C2 | semidirect |
| 14. C2×AΓL(1,𝔽9) | C4 | semidirect |
| 36. C2×PSU(3,𝔽2) | C2×C4 | semidirect |
| 48. C2×AGL(1,𝔽9) | C2×C4 | semidirect |
| 98. C2×C32×C4 | SD16 | semidirect |
| 99. C2×C3⋊Dic3 | SD16 | semidirect |
| 252. C32 | #1877 | semidirect |
| 292. C2×C4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×AΓL(1,𝔽9) | 2 |
| C2×C4×GO+(4,𝔽2) | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10593555 | 2 |
| #10593267 | 2 |
| #10593166 | 2 |
| #1877 | 9 |