Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C2×#41×C163 | C2 |
| hypercenter | C2×#41 | D163 |
| hypocenter | C163 | #547 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579698 | C2 | semidirect |
| 2. #19104733 | C2 | semidirect |
| 3. #19104718 | C2 | semidirect |
| 4. #19104716 | C2 | semidirect |
| 5. #19104714 | C2 | semidirect |
| 6. #19104711 | C2 | semidirect |
| 7. #19104707 | C2 | semidirect |
| 8. D4×Dic163 | C2 | semidirect |
| 9. C4×C22⋊D163 | C2 | semidirect |
| 10. C2×Dic163⋊C4 | C2 | semidirect |
| 11. C2×#41×C163 | C2 | semidirect |
| 53. D4×C163 | D4 | semidirect |
| 76. Dic163 | #41 | semidirect |
| 83. C163 | #547 | semidirect |
| 86. C2×#41 | D163 | semidirect |
| 129. D4 | C22⋊D163 | semidirect |