Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 161 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 | C2×#121×C79 | C2 |
| hypercenter | C2×#121 | D79 |
| hypocenter | C79 | #2543 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579133 | C2 | semidirect |
| 2. C2×C4×C22⋊D79 | C2 | semidirect |
| 3. #19098494 | C2 | semidirect |
| 4. #19098489 | C2 | semidirect |
| 5. #19098477 | C2 | semidirect |
| 6. #19098471 | C2 | semidirect |
| 7. #19098451 | C2 | semidirect |
| 8. #19098443 | C2 | semidirect |
| 9. #19098439 | C2 | semidirect |
| 10. C2×C79⋊#95 | C2 | semidirect |
| 11. C2×#121×C79 | C2 | semidirect |
| 44. C2×C22⋊D79 | D4 | semidirect |
| 72. C22×C4×C79 | D4 | semidirect |
| 162. C79 | #2543 | semidirect |
| 164. C2×#121 | D79 | semidirect |
| 225. C22×C4 | C22⋊D79 | semidirect |