Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×D107 |
| commutator, socle | C22×C107 | C24 |
| Fitting | #127×C107 | C2 |
| hypercenter | #127 | D107 |
| hypocenter | C107 | #535 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133817 | C2 | semidirect |
| 2. C2×D4×D107 | C2 | semidirect |
| 3. #16812105 | C2 | semidirect |
| 4. #16812097 | C2 | semidirect |
| 5. #16812096 | C2 | semidirect |
| 6. #16812081 | C2 | semidirect |
| 7. #16812077 | C2 | semidirect |
| 8. #16812066 | C2 | semidirect |
| 9. #127×C107 | C2 | semidirect |
| 12. C2×Dic214 | C22 | semidirect |
| 16. C2×C22⋊D107 | C22 | semidirect |
| 18. C22×Dic107 | C22 | semidirect |
| 20. Dic107⋊C4 | C22 | semidirect |
| 21. C22⋊Dic107 | C22 | semidirect |
| 23. (C2×D107)⋊C4 | C22 | semidirect |
| 24. C4×Dic107 | C22 | semidirect |
| 26. C2×D4×C107 | C22 | semidirect |
| 27. C2×D4×C107 | C22 | semidirect |
| 28. C42×C107 | C22 | semidirect |
| 48. C4×D107 | D4 | semidirect |
| 71. C107 | #535 | semidirect |
| 76. #127 | D107 | semidirect |
| 91. C2×D4 | C2×D107 | semidirect |
| 92. C2×D4 | C2×D107 | semidirect |
| 100. C42 | C2×D107 | semidirect |