Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #382×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C22×D316 | C22 |
| hypercenter | #382 | D79 |
| hypocenter | C79 | #2379 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19098467 | C2 | semidirect |
| 3. #19098455 | C2 | semidirect |
| 4. #19098453 | C2 | semidirect |
| 6. #19098437 | C2 | semidirect |
| 7. #19098434 | C2 | semidirect |
| 8. #19098429 | C2 | semidirect |
| 9. #382×C79 | C2 | semidirect |
| 13. #14579149 | C4 | semidirect |
| 35. C2×Dic158 | C2×C4 | semidirect |
| 51. (C2×D79)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D79)⋊C4 | C2×C4 | semidirect |
| 61. C42×C79 | C2×C4 | semidirect |
| 128. C79 | #2379 | semidirect |
| 137. #382 | D79 | semidirect |
| 189. C42 | C4×D79 | semidirect |