Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #386×C79 | C2 |
| prime radical | C2×#14579129 | C2 |
| hypercenter | #386 | D79 |
| hypocenter | C79 | #2684 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579148 | C2 | semidirect |
| 3. #19098488 | C2 | semidirect |
| 4. #19098479 | C2 | semidirect |
| 5. #19098476 | C2 | semidirect |
| 6. #19098455 | C2 | semidirect |
| 7. #19098442 | C2 | semidirect |
| 8. #19098418 | C2 | semidirect |
| 9. #386×C79 | C2 | semidirect |
| 11. C22×Dic158 | C22 | semidirect |
| 15. C2×C4⋊Dic79 | C22 | semidirect |
| 18. C2×C22⋊Dic79 | C22 | semidirect |
| 24. C2×C4×Dic79 | C22 | semidirect |
| 25. C79⋊#95 | C22 | semidirect |
| 26. C79⋊#95 | C22 | semidirect |
| 27. C79⋊#95 | C22 | semidirect |
| 29. C23×C4×C79 | C22 | semidirect |
| 31. C2×C22⋊C4×C79 | C22 | semidirect |
| 32. #95×C79 | C22 | semidirect |
| 153. C79 | #2684 | semidirect |
| 161. #386 | D79 | semidirect |
| 167. C23×C4 | C2×D79 | semidirect |
| 180. C2×C22⋊C4 | C2×D79 | semidirect |
| 185. #95 | C2×D79 | semidirect |