Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #384×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C22×D316 | C22 |
| hypercenter | #384 | D79 |
| hypocenter | C79 | #2326 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14579126 | C2 | semidirect |
| 4. #19098468 | C2 | semidirect |
| 6. #19098453 | C2 | semidirect |
| 7. #19098434 | C2 | semidirect |
| 8. #19098409 | C2 | semidirect |
| 9. #384×C79 | C2 | semidirect |
| 13. #14579149 | C4 | semidirect |
| 33. C2×Dic158 | C2×C4 | semidirect |
| 46. (C2×D79)⋊C4 | C2×C4 | semidirect |
| 57. C42×C79 | C2×C4 | semidirect |
| 112. C79 | #2326 | semidirect |
| 120. #384 | D79 | semidirect |
| 169. C42 | C4×D79 | semidirect |