Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 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×D139 |
| commutator, socle | C22×C139 | C24 |
| Fitting | #123×C139 | C2 |
| hypercenter | #123 | D139 |
| hypocenter | C139 | #525 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555784 | C2 | semidirect |
| 2. C22×C4×D139 | C2 | semidirect |
| 3. #17984825 | C2 | semidirect |
| 4. #17984820 | C2 | semidirect |
| 5. #17984815 | C2 | semidirect |
| 6. #17984812 | C2 | semidirect |
| 7. #17984810 | C2 | semidirect |
| 8. #17984804 | C2 | semidirect |
| 9. (C22⋊D139)⋊C4 | C2 | semidirect |
| 10. #17984798 | C2 | semidirect |
| 11. #123×C139 | C2 | semidirect |
| 14. C2×Dic278 | C22 | semidirect |
| 18. C2×C22⋊D139 | C22 | semidirect |
| 20. C22×Dic139 | C22 | semidirect |
| 24. C2×C4×D139 | C22 | semidirect |
| 25. Dic139⋊C4 | C22 | semidirect |
| 26. Dic139⋊C4 | C22 | semidirect |
| 30. (C2×D139)⋊C4 | C22 | semidirect |
| 31. C4×Dic139 | C22 | semidirect |
| 34. C4⋊C4×C139 | C22 | semidirect |
| 36. C22⋊C4×C139 | C22 | semidirect |
| 47. C2×Dic139 | D4 | semidirect |
| 72. C2×D139 | #41 | semidirect |
| 86. C139 | #525 | semidirect |
| 91. #123 | D139 | semidirect |
| 116. C4⋊C4 | C2×D139 | semidirect |
| 122. C22⋊C4 | C2×D139 | semidirect |