Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×D139 |
| commutator, socle | C22×C139 | C24 |
| Fitting | C4×D4×C139 | C2 |
| hypercenter | C4×D4 | D139 |
| hypocenter | C139 | #551 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984837 | C2 | semidirect |
| 2. #17984836 | C2 | semidirect |
| 3. #17984828 | C2 | semidirect |
| 4. #17984825 | C2 | semidirect |
| 5. #17984824 | C2 | semidirect |
| 6. #17984823 | C2 | semidirect |
| 7. #17984821 | C2 | semidirect |
| 8. #17984820 | C2 | semidirect |
| 10. C4×C22⋊D139 | C2 | semidirect |
| 11. #17984799 | C2 | semidirect |
| 12. #17984798 | C2 | semidirect |
| 13. C2×(C2×D139)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D139 | C2 | semidirect |
| 15. C4×D4×C139 | C2 | semidirect |
| 17. C2×Dic278 | C22 | semidirect |
| 23. C4⋊Dic139 | C22 | semidirect |
| 24. Dic139⋊C4 | C22 | semidirect |
| 25. Dic139⋊C4 | C22 | semidirect |
| 26. Dic139⋊C4 | C22 | semidirect |
| 27. Dic139⋊C4 | C22 | semidirect |
| 28. Dic139⋊C4 | C22 | semidirect |
| 29. Dic139⋊C4 | C22 | semidirect |
| 32. C22⋊Dic139 | C22 | semidirect |
| 33. C22⋊Dic139 | C22 | semidirect |
| 42. C4×Dic139 | C22 | semidirect |
| 43. C4×Dic139 | C22 | semidirect |
| 46. C22×C4×C139 | C22 | semidirect |
| 47. C4⋊C4×C139 | C22 | semidirect |
| 49. C22⋊C4×C139 | C22 | semidirect |
| 50. C42×C139 | C22 | semidirect |
| 110. C139 | #551 | semidirect |
| 122. C4×D4 | D139 | semidirect |
| 136. C22×C4 | C2×D139 | semidirect |
| 144. C4⋊C4 | C2×D139 | semidirect |
| 158. C22⋊C4 | C2×D139 | semidirect |
| 161. C42 | C2×D139 | semidirect |