Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
204 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14579134 |
| commutator, cosocle | C42×C79 | C23 |
| Frattini | C42 | C22×D79 |
| Fitting | #331×C79 | C2 |
| socle | C22×C79 | #121 |
| hypercenter | #331 | D79 |
| hypocenter | C79 | #1667 |
| LCS | G ▷ C42×C79 ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #331 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19098939 | C2 | semidirect |
| 2. #19098759 | C2 | semidirect |
| 3. #19098755 | C2 | semidirect |
| 4. #19098628 | C2 | semidirect |
| 5. #19098315 | C2 | semidirect |
| 6. #19098306 | C2 | semidirect |
| 7. #331×C79 | C2 | semidirect |
| 62. D316 | D8 | semidirect |
| 69. C79⋊C8 | D8 | semidirect |
| 93. C79 | #1667 | semidirect |
| 100. #331 | D79 | semidirect |