Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
948 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 185 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×#127×C79 | C2 |
| hypercenter | C2×#127 | D79 |
| hypocenter | C79 | #2541 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579157 | C2 | semidirect |
| 2. C2×#14579157 | C2 | semidirect |
| 3. C2×#14579133 | C2 | semidirect |
| 4. C2×D4×Dic79 | C2 | semidirect |
| 5. #19098471 | C2 | semidirect |
| 6. #19098466 | C2 | semidirect |
| 7. #19098465 | C2 | semidirect |
| 8. C4×Dic79⋊C4 | C2 | semidirect |
| 9. C2×#127×C79 | C2 | semidirect |
| 50. Dic79⋊C4 | D4 | semidirect |
| 55. C4×Dic79 | D4 | semidirect |
| 66. C2×D4×C79 | D4 | semidirect |
| 130. C4×C79 | #121 | semidirect |
| 134. Dic79 | #127 | semidirect |
| 144. C79 | #2541 | semidirect |
| 147. C2×#127 | D79 | semidirect |
| 197. C2×D4 | C22⋊D79 | semidirect |
| 278. C4 | #14579133 | semidirect |