Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
554 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
| 46. C32×C42 | Q8 | semidirect |
| 47. C4×C3⋊Dic3 | Q8 | semidirect |
| 48. C4×C3⋊Dic3 | Q8 | semidirect |
| 156. C42 | PSU(3,𝔽2) | semidirect |
| 166. C32 | #2295 | 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 |
| #10593733 | 2 |
| C42×#157 | 2 |
| #10593555 | 2 |
| #10593550 | 2 |
| C4×#3777 | 2 |
| #10593548 | 2 |
| #2295 | 9 |