Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
502 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 502 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 |
|---|---|---|
| 5. #10596404 | C2 | direct (N × H) |
| 113. C2×C32 | #487 | semidirect |
| 115. C3⋊D3 | #487 | semidirect |
| 148. C32 | C2×#487 | semidirect |
| 190. C2 | #10596404 | 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×PSU(3,𝔽2)⋊C4 | 2 |
| #10596404 | 2 |
| C2×#487 | 9 |