Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
934 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 236 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. C2×PSU(3,𝔽2)⋊C4 | C2 | direct (N × H) |
| 9. C22×PSU(3,𝔽2) | C4 | semidirect |
| 16. PSU(3,𝔽2)⋊C4 | C22 | direct (N × H) |
| 27. C2×PSU(3,𝔽2) | C2×C4 | semidirect |
| 52. PSU(3,𝔽2) | C22×C4 | semidirect |
| 66. C22×C32 | #103 | semidirect |
| 68. C2×C3⋊D3 | #103 | semidirect |
| 99. C2×C32 | C2×#103 | semidirect |
| 101. C3⋊D3 | C2×#103 | semidirect |
| 132. C32 | C22×#103 | semidirect |
| 162. C22 | PSU(3,𝔽2)⋊C4 | direct (N × H) |
| 173. C2 | C2×PSU(3,𝔽2)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2) | 2 |
| C23×AGL(1,𝔽9) | 2 |
| C22×#3773 | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| C22×#103 | 9 |