Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
440 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 2. C2×C4×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 6. #10593267 | C2 | semidirect |
| 7. #10593166 | C2 | semidirect |
| 14. C2×AΓL(1,𝔽9) | C4 | semidirect |
| 91. PSU(3,𝔽2) | C22⋊C4 | semidirect |
| 98. C2×C32×C4 | SD16 | semidirect |
| 99. C2×C3⋊Dic3 | SD16 | semidirect |
| 244. C32 | #1880 | semidirect |
| 282. 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×PSU(3,𝔽2) | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10593454 | 2 |
| #10593267 | 2 |
| #10593166 | 2 |
| #1880 | 9 |