Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
378 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 11. C4⋊PSU(3,𝔽2) | C4 | semidirect |
| 77. C32×C4 | #103 | semidirect |
| 78. C3⋊Dic3 | #103 | semidirect |
| 134. C32 | #1981 | semidirect |
| 172. C4 | PSU(3,𝔽2)⋊C4 | semidirect |
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×C4⋊AGL(1,𝔽9) | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| C4×#3773 | 2 |
| #1981 | 9 |