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 | C22⋊Q8×C139 | C2 |
| hypercenter | C22⋊Q8 | D139 |
| hypocenter | C139 | #551 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984837 | C2 | semidirect |
| 2. #17984837 | C2 | semidirect |
| 3. #17984831 | C2 | semidirect |
| 4. #17984827 | C2 | semidirect |
| 5. #17984827 | C2 | semidirect |
| 6. #17984826 | C2 | semidirect |
| 7. #17984818 | C2 | semidirect |
| 9. #17984804 | C2 | semidirect |
| 10. C4×C22⋊D139 | C2 | semidirect |
| 11. #17984800 | C2 | semidirect |
| 12. #17984798 | C2 | semidirect |
| 13. C2×(C2×D139)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D139 | C2 | semidirect |
| 15. C22⋊Q8×C139 | C2 | semidirect |
| 23. C2×C4×D139 | C22 | semidirect |
| 24. C4⋊Dic139 | C22 | semidirect |
| 25. C4⋊Dic139 | C22 | semidirect |
| 26. Dic139⋊C4 | C22 | semidirect |
| 27. Dic139⋊C4 | C22 | semidirect |
| 28. Dic139⋊C4 | C22 | semidirect |
| 38. (C2×D139)⋊C4 | C22 | semidirect |
| 39. (C2×D139)⋊C4 | C22 | semidirect |
| 40. (C2×D139)⋊C4 | C22 | semidirect |
| 41. C4×Dic139 | C22 | semidirect |
| 42. C4×Dic139 | C22 | semidirect |
| 43. C4×Dic139 | C22 | semidirect |
| 44. C2×Q8×C139 | C22 | semidirect |
| 46. C4⋊C4×C139 | C22 | semidirect |
| 47. C4⋊C4×C139 | C22 | semidirect |
| 48. C4⋊C4×C139 | C22 | semidirect |
| 110. C139 | #551 | semidirect |
| 119. C22⋊Q8 | D139 | semidirect |
| 128. C2×Q8 | C2×D139 | semidirect |
| 142. C4⋊C4 | C2×D139 | semidirect |
| 143. C4⋊C4 | C2×D139 | semidirect |
| 144. C4⋊C4 | C2×D139 | semidirect |