Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
628 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 628 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 | #383×C79 | C2 |
| hypercenter | #383 | D79 |
| hypocenter | C79 | #2631 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579149 | C2 | semidirect |
| 2. C2×C4×D316 | C2 | semidirect |
| 3. #19098490 | C2 | semidirect |
| 4. #19098476 | C2 | semidirect |
| 5. #19098473 | C2 | semidirect |
| 6. #19098473 | C2 | semidirect |
| 7. #19098441 | C2 | semidirect |
| 8. #383×C79 | C2 | semidirect |
| 52. C42×C79 | D4 | semidirect |
| 109. C79 | #2631 | semidirect |
| 117. #383 | D79 | semidirect |
| 161. C42 | D316 | semidirect |