Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
446 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10593166 | C2 | semidirect |
| 13. C22⋊PSU(3,𝔽2) | C4 | semidirect |
| 86. C22×C32 | #103 | semidirect |
| 92. C2×C3⋊D3 | #103 | semidirect |
| 176. C32 | #1892 | semidirect |
| 221. C22 | PSU(3,𝔽2)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽9) | 2 |
| C2×C22⋊PSU(3,𝔽2) | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| #10593516 | 2 |
| #10593166 | 2 |
| #1892 | 9 |