Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812155 | C2 | semidirect |
| 2. #16812135 | C2 | semidirect |
| 3. #16812134 | C2 | semidirect |
| 4. #16812129 | C2 | semidirect |
| 5. C2×#13133803 | C2 | semidirect |
| 6. #16812116 | C2 | semidirect |
| 7. H(5,𝔽2)×C107 | C2 | semidirect |
| 9. #13133818 | C22 | semidirect |
| 10. C2×D428 | C22 | semidirect |
| 12. #13133808 | C22 | semidirect |
| 13. #13133806 | C22 | semidirect |
| 14. #13133805 | C22 | semidirect |
| 15. #13133803 | C22 | semidirect |
| 16. #13133803 | C22 | semidirect |
| 17. #13133802 | C22 | semidirect |
| 18. C2×C107⋊C8 | C22 | semidirect |
| 21. #41×C107 | C22 | semidirect |
| 23. C2×D4×C107 | C22 | semidirect |
| 54. C107 | #576 | semidirect |
| 57. H(5,𝔽2) | D107 | semidirect |
| 67. #41 | C2×D107 | semidirect |
| 71. C2×D4 | C2×D107 | semidirect |