Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
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×D137 |
| commutator, socle | C22×C137 | C24 |
| Fitting | C22×D4×C137 | C2 |
| hypercenter | C22×D4 | D137 |
| hypocenter | C137 | #546 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555509 | C2 | semidirect |
| 2. #17984075 | C2 | semidirect |
| 3. #17984069 | C2 | semidirect |
| 4. #17984067 | C2 | semidirect |
| 5. #17984060 | C2 | semidirect |
| 6. #17984059 | C2 | semidirect |
| 7. #17984057 | C2 | semidirect |
| 8. D4×Dic137 | C2 | semidirect |
| 9. C4×C22⋊D137 | C2 | semidirect |
| 10. C2×C22⋊Dic137 | C2 | semidirect |
| 11. C22×D4×C137 | C2 | semidirect |
| 13. C2×Dic274 | C22 | semidirect |
| 15. C2×C22⋊D137 | C22 | semidirect |
| 16. C2×C22⋊D137 | C22 | semidirect |
| 17. C22×Dic137 | C22 | semidirect |
| 18. C22×Dic137 | C22 | semidirect |
| 19. C2×C4×D137 | C22 | semidirect |
| 20. C4⋊Dic137 | C22 | semidirect |
| 21. #14555489 | C22 | semidirect |
| 22. #14555489 | C22 | semidirect |
| 25. C22⋊Dic137 | C22 | semidirect |
| 26. C22⋊Dic137 | C22 | semidirect |
| 27. C22⋊Dic137 | C22 | semidirect |
| 28. C22⋊Dic137 | C22 | semidirect |
| 29. #14555487 | C22 | semidirect |
| 30. C4×Dic137 | C22 | semidirect |
| 58. D4×C137 | D4 | semidirect |
| 71. C22×C137 | #41 | semidirect |
| 90. C137 | #546 | semidirect |
| 93. C22×D4 | D137 | semidirect |
| 141. D4 | C22⋊D137 | semidirect |
| 165. C22 | #14555509 | semidirect |