Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #123×C151 | C2 |
| hypercenter | #123 | D151 |
| hypocenter | C151 | #547 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14559004 | C2 | semidirect |
| 2. C2×#14559003 | C2 | semidirect |
| 3. #18012738 | C2 | semidirect |
| 4. #18012724 | C2 | semidirect |
| 5. #18012723 | C2 | semidirect |
| 6. #18012721 | C2 | semidirect |
| 7. #18012717 | C2 | semidirect |
| 8. #18012716 | C2 | semidirect |
| 9. #18012712 | C2 | semidirect |
| 10. #18012711 | C2 | semidirect |
| 11. (C22⋊D151)⋊C4 | C2 | semidirect |
| 12. (C22⋊D151)⋊C4 | C2 | semidirect |
| 13. C2×Dic151⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D151 | C2 | semidirect |
| 15. #123×C151 | C2 | semidirect |
| 61. C22⋊D151 | D4 | semidirect |
| 107. Dic151 | #41 | semidirect |
| 115. C151 | #547 | semidirect |
| 123. #123 | D151 | semidirect |