Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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 | #384×C79 | C2 |
| prime radical | C22×D316 | C22 |
| hypercenter | #384 | D79 |
| hypocenter | C79 | #2542 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579160 | C2 | semidirect |
| 2. C2×#14579139 | C2 | semidirect |
| 4. #19098498 | C2 | semidirect |
| 7. #19098432 | C2 | semidirect |
| 8. C4×Dic79⋊C4 | C2 | semidirect |
| 9. #384×C79 | C2 | semidirect |
| 35. C2×D316 | Q8 | semidirect |
| 45. Dic79⋊C4 | D4 | semidirect |
| 100. C4×C79 | C22⋊Q8 | semidirect |
| 112. C79 | #2542 | semidirect |
| 120. #384 | D79 | semidirect |
| 216. C4 | #14579139 | semidirect |