Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #381×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C24×C79 | C23 |
| hypercenter | #381 | D79 |
| hypocenter | C79 | #2378 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19098467 | C2 | semidirect |
| 3. #19098460 | C2 | semidirect |
| 6. #19098450 | C2 | semidirect |
| 7. #19098448 | C2 | semidirect |
| 11. #14579140 | C4 | semidirect |
| 111. C79 | #2378 | semidirect |