Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting, prime radical | #120×C167 | C2 |
| hypercenter | #120 | D167 |
| hypocenter | C167 | #551 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128825 | C2 | semidirect |
| 2. #19128819 | C2 | semidirect |
| 3. #19128813 | C2 | semidirect |
| 4. #19128813 | C2 | semidirect |
| 5. #19128809 | C2 | semidirect |
| 6. D4×Dic167 | C2 | semidirect |
| 7. #19128788 | C2 | semidirect |
| 8. C2×C22⋊Dic167 | C2 | semidirect |
| 10. C2×Dic334 | C22 | semidirect |
| 13. C22×Dic167 | C22 | semidirect |
| 14. C4⋊Dic167 | C22 | semidirect |
| 15. Dic167⋊C4 | C22 | semidirect |
| 16. Dic167⋊C4 | C22 | semidirect |
| 17. Dic167⋊C4 | C22 | semidirect |
| 22. C22⋊Dic167 | C22 | semidirect |
| 23. C22⋊Dic167 | C22 | semidirect |
| 24. C4×Dic167 | C22 | semidirect |
| 25. C4×Dic167 | C22 | semidirect |
| 68. C167 | #551 | semidirect |