Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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, socle, cosocle | C23×C79 | C24 |
| Fitting | #390×C79 | C2 |
| prime radical | C22×D4×C79 | C22 |
| hypercenter | #390 | D79 |
| hypocenter | C79 | #2644 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19098491 | C2 | semidirect |
| 2. #19098491 | C2 | semidirect |
| 3. #19098488 | C2 | semidirect |
| 4. #19098486 | C2 | semidirect |
| 7. #19098462 | C2 | semidirect |
| 8. #19098461 | C2 | semidirect |
| 9. #19098459 | C2 | semidirect |
| 10. #19098409 | C2 | semidirect |
| 136. C79 | #2644 | semidirect |