Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
850 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#157 |
| commutator, socle | C22×C32 | C23×C4 |
| Fitting | C32×C4×Q8 | C4 |
| prime radical, cosocle | C22×C3⋊D3 | C24 |
| hypercenter | C4×Q8 | #157 |
| hypocenter | C32 | #2351 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C32×C4×Q8 | C4 | semidirect |
| 12. Q8×C3⋊Dic3 | C4 | semidirect |
| 14. #64096 | C4 | semidirect |
| 16. C4×#634 | C4 | semidirect |
| 55. C32×Q8 | C4⋊C4 | semidirect |
| 66. #634 | C4⋊C4 | semidirect |
| 104. C4×Q8 | #157 | semidirect |
| 161. C32 | #2351 | semidirect |
| 164. Q8 | C4⋊#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| C4×Q8×C3⋊D3 | 2 |
| #10593759 | 2 |
| #10593736 | 2 |
| C4×C4⋊#157 | 2 |
| #2351 | 9 |