Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
494 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 6. PSU(3,𝔽2)⋊Q8 | C2 | direct (N × H) |
| 29. C2×PSU(3,𝔽2) | Q8 | semidirect |
| 63. PSU(3,𝔽2) | C2×Q8 | semidirect |
| 129. C2×C32 | #475 | semidirect |
| 131. C3⋊D3 | #475 | semidirect |
| 168. C32 | C2×#475 | semidirect |
| 216. C2 | PSU(3,𝔽2)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×#64222 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C2×AGL(1,𝔽9)⋊C4 | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| PSU(3,𝔽2)⋊Q8 | 2 |
| C2×#475 | 9 |