Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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×D79 |
| commutator, socle | C22×C79 | C24 |
| Fitting | #123×C79 | C2 |
| hypercenter | #123 | D79 |
| hypocenter | C79 | #562 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14579152 | C2 | semidirect |
| 2. #14579147 | C2 | semidirect |
| 3. #14579147 | C2 | semidirect |
| 4. #14579146 | C2 | semidirect |
| 5. #14579145 | C2 | semidirect |
| 6. #14579143 | C2 | semidirect |
| 7. #14579141 | C2 | semidirect |
| 8. #14579140 | C2 | semidirect |
| 9. #14579139 | C2 | semidirect |
| 10. #14579138 | C2 | semidirect |
| 11. #14579135 | C2 | semidirect |
| 12. #14579134 | C2 | semidirect |
| 13. #14579133 | C2 | semidirect |
| 14. #14579132 | C2 | semidirect |
| 15. #123×C79 | C2 | semidirect |
| 109. C79 | #562 | semidirect |
| 117. #123 | D79 | semidirect |