Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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×D107 |
| commutator | C4×C107 | C24 |
| Frattini | C4 | C23×D107 |
| Fitting | C2×D8×C107 | C2 |
| socle | C2×C107 | C22×D4 |
| hypercenter | C2×D8 | D107 |
| hypocenter | C107 | #576 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812154 | C2 | semidirect |
| 2. #16812135 | C2 | semidirect |
| 3. #16812133 | C2 | semidirect |
| 4. #16812131 | C2 | semidirect |
| 5. #16812128 | C2 | semidirect |
| 6. D8×D107 | C2 | semidirect |
| 7. #16812115 | C2 | semidirect |
| 8. C2×D8×C107 | C2 | semidirect |
| 10. #13133818 | C22 | semidirect |
| 12. #13133817 | C22 | semidirect |
| 15. D4×D107 | C22 | semidirect |
| 16. Dic428 | C22 | semidirect |
| 17. #13133807 | C22 | semidirect |
| 18. #13133806 | C22 | semidirect |
| 19. D856 | C22 | semidirect |
| 20. #13133803 | C22 | semidirect |
| 21. #13133802 | C22 | semidirect |
| 22. #13133801 | C22 | semidirect |
| 23. C8×D107 | C22 | semidirect |
| 24. C2×D4×C107 | C22 | semidirect |
| 25. D8×C107 | C22 | semidirect |
| 26. D8×C107 | C22 | semidirect |
| 27. C2×C8×C107 | C22 | semidirect |
| 62. C107 | #576 | semidirect |
| 70. C2×D8 | D107 | semidirect |
| 79. C2×D4 | C2×D107 | semidirect |
| 85. D8 | C2×D107 | semidirect |
| 86. D8 | C2×D107 | semidirect |
| 90. C2×C8 | C2×D107 | semidirect |