Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C4×D4×C167 | C2 |
| hypercenter | C4×D4 | D167 |
| hypocenter | C167 | #546 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581950 | C2 | semidirect |
| 2. C22×D668 | C2 | semidirect |
| 3. #19128820 | C2 | semidirect |
| 4. #19128817 | C2 | semidirect |
| 5. #19128811 | C2 | semidirect |
| 6. #19128806 | C2 | semidirect |
| 7. #19128805 | C2 | semidirect |
| 8. #19128800 | C2 | semidirect |
| 9. C4×D668 | C2 | semidirect |
| 10. C22⋊C4×D167 | C2 | semidirect |
| 11. C4×D4×C167 | C2 | semidirect |
| 14. C2×Dic334 | C22 | semidirect |
| 19. C2×C22⋊D167 | C22 | semidirect |
| 20. C2×C22⋊D167 | C22 | semidirect |
| 21. C2×C4×D167 | C22 | semidirect |
| 22. C2×C4×D167 | C22 | semidirect |
| 23. C4⋊Dic167 | C22 | semidirect |
| 24. Dic167⋊C4 | C22 | semidirect |
| 26. (C2×D167)⋊C4 | C22 | semidirect |
| 27. (C2×D167)⋊C4 | C22 | semidirect |
| 28. (C2×D167)⋊C4 | C22 | semidirect |
| 29. (C2×D167)⋊C4 | C22 | semidirect |
| 32. C22×C4×C167 | C22 | semidirect |
| 33. C4⋊C4×C167 | C22 | semidirect |
| 35. C22⋊C4×C167 | C22 | semidirect |
| 36. C42×C167 | C22 | semidirect |
| 45. D668 | D4 | semidirect |
| 67. C22×C167 | #41 | semidirect |
| 90. C167 | #546 | semidirect |
| 101. C4×D4 | D167 | semidirect |
| 116. C22×C4 | C2×D167 | semidirect |
| 119. C4⋊C4 | C2×D167 | semidirect |
| 126. C22⋊C4 | C2×D167 | semidirect |
| 127. C42 | C2×D167 | semidirect |
| 165. C22 | #14581950 | semidirect |