Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, cosocle | C22×C163 | C24 |
| Fitting | #123×C163 | C2 |
| hypercenter | #123 | D163 |
| hypocenter | C163 | #547 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579699 | C2 | semidirect |
| 2. C2×#14579698 | C2 | semidirect |
| 3. #19104734 | C2 | semidirect |
| 4. #19104720 | C2 | semidirect |
| 5. #19104719 | C2 | semidirect |
| 6. #19104717 | C2 | semidirect |
| 7. #19104713 | C2 | semidirect |
| 8. #19104712 | C2 | semidirect |
| 9. #19104708 | C2 | semidirect |
| 10. #19104707 | C2 | semidirect |
| 11. (C22⋊D163)⋊C4 | C2 | semidirect |
| 12. (C22⋊D163)⋊C4 | C2 | semidirect |
| 13. C2×Dic163⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D163 | C2 | semidirect |
| 15. #123×C163 | C2 | semidirect |
| 61. C22⋊D163 | D4 | semidirect |
| 107. Dic163 | #41 | semidirect |
| 115. C163 | #547 | semidirect |
| 123. #123 | D163 | semidirect |