Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D139 |
| commutator | C4×C139 | C24 |
| Frattini | C4 | C23×D139 |
| Fitting | #137×C139 | C2 |
| socle | C2×C139 | C22×D4 |
| hypercenter | #137 | D139 |
| hypocenter | C139 | #577 |
| LCS | G ▷ C4×C139 ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984890 | C2 | semidirect |
| 2. #17984888 | C2 | semidirect |
| 3. #17984874 | C2 | semidirect |
| 4. #17984870 | C2 | semidirect |
| 5. #17984869 | C2 | semidirect |
| 6. #17984865 | C2 | semidirect |
| 7. #17984862 | C2 | semidirect |
| 8. C2×#14555772 | C2 | semidirect |
| 9. SD16×D139 | C2 | semidirect |
| 10. #17984850 | C2 | semidirect |
| 11. #137×C139 | C2 | semidirect |
| 14. #14555786 | C22 | semidirect |
| 18. #14555785 | C22 | semidirect |
| 20. Q8×D139 | C22 | semidirect |
| 25. #14555775 | C22 | semidirect |
| 26. #14555774 | C22 | semidirect |
| 27. #14555773 | C22 | semidirect |
| 28. #14555772 | C22 | semidirect |
| 29. #14555772 | C22 | semidirect |
| 30. #14555772 | C22 | semidirect |
| 31. D1112 | C22 | semidirect |
| 32. #14555770 | C22 | semidirect |
| 33. #14555768 | C22 | semidirect |
| 34. C2×C139⋊C8 | C22 | semidirect |
| 35. C8×D139 | C22 | semidirect |
| 37. C2×Q8×C139 | C22 | semidirect |
| 38. Q16×C139 | C22 | semidirect |
| 39. SD16×C139 | C22 | semidirect |
| 40. M16×C139 | C22 | semidirect |
| 90. C139 | #577 | semidirect |
| 95. #137 | D139 | semidirect |
| 113. C2×Q8 | C2×D139 | semidirect |
| 119. Q16 | C2×D139 | semidirect |
| 125. SD16 | C2×D139 | semidirect |
| 129. M16 | C2×D139 | semidirect |