Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #392×C79 | C2 |
| hypercenter | #392 | D79 |
| hypocenter | C79 | #2388 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11929623 | C2 | semidirect |
| 2. C2×D4×Dic79 | C2 | semidirect |
| 3. C2×(C22⋊D79)⋊C4 | C2 | semidirect |
| 4. #19098484 | C2 | semidirect |
| 5. #19098479 | C2 | semidirect |
| 6. #19098477 | C2 | semidirect |
| 7. #19098475 | C2 | semidirect |
| 8. #19098471 | C2 | semidirect |
| 9. C22⋊C4×Dic79 | C2 | semidirect |
| 10. #19098410 | C2 | semidirect |
| 11. #392×C79 | C2 | semidirect |
| 53. C22×Dic79 | D4 | semidirect |
| 60. C2×C4×D79 | D4 | semidirect |
| 93. C23×C79 | #41 | semidirect |
| 108. C2×C4×C79 | #41 | semidirect |
| 125. C2×Dic79 | #41 | semidirect |
| 167. C79 | #2388 | semidirect |
| 176. #392 | D79 | semidirect |
| 265. C23 | #11929623 | semidirect |
| 294. C2×C4 | #11929623 | semidirect |