Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 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, prime radical | C23×D4×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| hypercenter | C23×D4 | D79 |
| hypocenter | C79 | #2308 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic79 | C2 | semidirect |
| 2. #19098443 | C2 | semidirect |
| 3. #19098426 | C2 | semidirect |
| 4. #19098419 | C2 | semidirect |
| 6. C23×Dic79 | C22 | semidirect |
| 9. C2×C22⋊Dic79 | C22 | semidirect |
| 10. C2×C22⋊Dic79 | C22 | semidirect |
| 11. C79⋊#95 | C22 | semidirect |
| 15. C22×D4×C79 | C4 | semidirect |
| 28. C24×C79 | C2×C4 | semidirect |
| 36. C2×D4×C79 | C2×C4 | semidirect |
| 38. C22×C4×C79 | C2×C4 | semidirect |
| 49. C23×C79 | C22⋊C4 | semidirect |
| 88. C79 | #2308 | semidirect |
| 97. C22×D4 | Dic79 | semidirect |
| 110. C24 | C2×Dic79 | semidirect |
| 118. C2×D4 | C2×Dic79 | semidirect |
| 123. C22×C4 | C2×Dic79 | semidirect |
| 137. C23 | C22⋊Dic79 | semidirect |