Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
646 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 646 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 |
|---|---|---|
| 1. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×C4×AGL(1,𝔽9) | C2 | semidirect |
| 4. C2×GO+(4,𝔽2)⋊C4 | C2 | semidirect |
| 5. #10596402 | C2 | direct (N × H) |
| 15. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 18. C4×AGL(1,𝔽9) | C22 | semidirect |
| 19. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 125. C2×C32 | #486 | semidirect |
| 127. C3⋊D3 | #486 | semidirect |
| 168. C32 | C2×#486 | semidirect |
| 221. C2 | #10596402 | 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×#64231 | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10596402 | 2 |
| C2×#486 | 9 |