Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C22×D4×C167 | C2 |
| hypercenter | C22×D4 | D167 |
| hypocenter | C167 | #546 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581949 | C2 | semidirect |
| 2. #19128819 | C2 | semidirect |
| 3. #19128813 | C2 | semidirect |
| 4. #19128811 | C2 | semidirect |
| 5. #19128804 | C2 | semidirect |
| 6. #19128803 | C2 | semidirect |
| 7. #19128801 | C2 | semidirect |
| 8. D4×Dic167 | C2 | semidirect |
| 9. C4×C22⋊D167 | C2 | semidirect |
| 10. C2×C22⋊Dic167 | C2 | semidirect |
| 11. C22×D4×C167 | C2 | semidirect |
| 13. C2×Dic334 | C22 | semidirect |
| 15. C2×C22⋊D167 | C22 | semidirect |
| 16. C2×C22⋊D167 | C22 | semidirect |
| 17. C22×Dic167 | C22 | semidirect |
| 18. C22×Dic167 | C22 | semidirect |
| 19. C2×C4×D167 | C22 | semidirect |
| 20. C4⋊Dic167 | C22 | semidirect |
| 21. Dic167⋊C4 | C22 | semidirect |
| 22. Dic167⋊C4 | C22 | semidirect |
| 25. C22⋊Dic167 | C22 | semidirect |
| 26. C22⋊Dic167 | C22 | semidirect |
| 27. C22⋊Dic167 | C22 | semidirect |
| 28. C22⋊Dic167 | C22 | semidirect |
| 29. (C2×D167)⋊C4 | C22 | semidirect |
| 30. C4×Dic167 | C22 | semidirect |
| 58. D4×C167 | D4 | semidirect |
| 71. C22×C167 | #41 | semidirect |
| 90. C167 | #546 | semidirect |
| 93. C22×D4 | D167 | semidirect |
| 141. D4 | C22⋊D167 | semidirect |
| 165. C22 | #14581949 | semidirect |