Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator | C22×C79 | C23×C4 |
| Fitting | #382×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C23×D79 | C23 |
| hypercenter | #382 | D79 |
| hypocenter | C79 | #2283 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19098430 | C2 | semidirect |
| 3. #19098429 | C2 | semidirect |
| 6. C4⋊C4×Dic79 | C2 | semidirect |
| 8. #19098408 | C2 | semidirect |
| 9. #382×C79 | C2 | semidirect |
| 19. C42×D79 | C4 | semidirect |
| 106. C79 | #2283 | semidirect |
| 110. #382 | D79 | semidirect |