Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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×D151 |
| commutator, socle, cosocle | C22×C151 | C24 |
| Fitting | C4⋊Q8×C151 | C2 |
| prime radical | C2×D604 | C22 |
| hypercenter | C4⋊Q8 | D151 |
| hypocenter | C151 | #554 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18012730 | C2 | semidirect |
| 2. #18012719 | C2 | semidirect |
| 3. #18012715 | C2 | semidirect |
| 4. C4×Dic302 | C2 | semidirect |
| 7. C4⋊C4×D151 | C2 | semidirect |
| 8. C4⋊Q8×C151 | C2 | semidirect |
| 27. D604 | Q8 | semidirect |
| 53. C151 | #554 | semidirect |
| 55. C4⋊Q8 | D151 | semidirect |