Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×D428 | C2 | semidirect |
| 2. #16812134 | C2 | direct (N × H) |
| 3. C2×#13133805 | C2 | semidirect |
| 4. C2×#13133803 | C2 | semidirect |
| 5. C2×#13133802 | C2 | semidirect |
| 6. C2×#41×C107 | C2 | semidirect |
| 11. C2×D428 | C22 | semidirect |
| 12. #13133805 | C22 | semidirect |
| 13. #13133803 | C22 | semidirect |
| 14. #13133802 | C22 | semidirect |
| 15. C2×C107⋊C8 | C22 | semidirect |
| 17. #41×C107 | C22 | semidirect |
| 18. C2×Q8×C107 | C22 | semidirect |
| 20. C2×D4×C107 | C22 | semidirect |
| 29. Q8×C107 | C23 | semidirect |
| 32. D4×C107 | C23 | semidirect |
| 42. C107⋊C8 | C23 | semidirect |
| 57. C2×C107 | AGL(1,ℤ/8) | semidirect |
| 60. C107 | C2×AGL(1,ℤ/8) | semidirect |
| 62. C2×#41 | D107 | semidirect |
| 70. #41 | C2×D107 | semidirect |
| 71. C2×Q8 | C2×D107 | semidirect |
| 77. C2×D4 | C2×D107 | semidirect |
| 90. Q8 | C22×D107 | semidirect |
| 96. D4 | C22×D107 | semidirect |
| 119. C2 | #16812134 | direct (N × H) |