Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
816 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #379×C79 | C2 |
| hypercenter | #379 | D79 |
| hypocenter | C79 | #2668 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579134 | C2 | semidirect |
| 2. C2×#14579130 | C2 | semidirect |
| 3. #19098499 | C2 | semidirect |
| 4. #19098491 | C2 | semidirect |
| 5. #19098479 | C2 | semidirect |
| 6. #19098472 | C2 | semidirect |
| 7. #19098439 | C2 | semidirect |
| 8. #19098439 | C2 | semidirect |
| 9. #379×C79 | C2 | semidirect |
| 10. C22×D316 | C22 | semidirect |
| 14. C22×C4×D79 | C22 | semidirect |
| 17. C2×C4⋊Dic79 | C22 | semidirect |
| 18. C2×Dic79⋊C4 | C22 | semidirect |
| 22. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 23. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 24. C79⋊#95 | C22 | semidirect |
| 25. C79⋊#95 | C22 | semidirect |
| 26. C79⋊#95 | C22 | semidirect |
| 27. C79⋊#95 | C22 | semidirect |
| 44. C2×C22⋊D79 | D4 | semidirect |
| 158. C79 | #2668 | semidirect |
| 167. #379 | D79 | semidirect |