Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C139 | C2 |
| hypercenter | #124 | D139 |
| hypocenter | C139 | #551 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984835 | C2 | semidirect |
| 2. #17984824 | C2 | semidirect |
| 3. #17984823 | C2 | semidirect |
| 4. #17984818 | C2 | semidirect |
| 6. (C22⋊D139)⋊C4 | C2 | semidirect |
| 7. #17984799 | C2 | semidirect |
| 8. C22⋊C4×D139 | C2 | semidirect |
| 9. #124×C139 | C2 | semidirect |
| 12. C22×Dic139 | C22 | semidirect |
| 15. C4⋊Dic139 | C22 | semidirect |
| 16. Dic139⋊C4 | C22 | semidirect |
| 17. Dic139⋊C4 | C22 | semidirect |
| 18. Dic139⋊C4 | C22 | semidirect |
| 21. C22⋊Dic139 | C22 | semidirect |
| 25. C4×Dic139 | C22 | semidirect |
| 26. C2×Q8×C139 | C22 | semidirect |
| 29. C22⋊C4×C139 | C22 | semidirect |
| 30. C42×C139 | C22 | semidirect |
| 68. C139 | #551 | semidirect |
| 71. #124 | D139 | semidirect |
| 80. C2×Q8 | C2×D139 | semidirect |
| 97. C22⋊C4 | C2×D139 | semidirect |
| 99. C42 | C2×D139 | semidirect |