Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
598 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 20. C4⋊PSU(3,𝔽2) | C4 | semidirect |
| 48. C32×C4⋊C4 | Q8 | semidirect |
| 49. C4⋊(C3⋊Dic3) | Q8 | semidirect |
| 50. #3750 | Q8 | semidirect |
| 108. C32×C4 | C4×Q8 | semidirect |
| 110. C3⋊Dic3 | C4×Q8 | semidirect |
| 164. C4⋊C4 | PSU(3,𝔽2) | semidirect |
| 180. C32 | #2365 | semidirect |
| 232. C4 | C4×PSU(3,𝔽2) | 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×PSU(3,𝔽2) | 2 |
| C4⋊C4×#157 | 2 |
| #10593555 | 2 |
| #10593554 | 2 |
| #10593550 | 2 |
| C4×#3777 | 2 |
| #2365 | 9 |