Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. M16×D109 | C2 | semidirect |
| 3. C42×D109 | C2 | semidirect |
| 4. #16812627 | C2 | semidirect |
| 5. #16812626 | C2 | semidirect |
| 6. #16812625 | C2 | semidirect |
| 7. #104×C109 | C2 | semidirect |
| 8. #13182030 | C4 | semidirect |
| 12. #13182028 | C4 | semidirect |
| 13. Q8×D109 | C4 | semidirect |
| 15. D4×D109 | C4 | semidirect |
| 19. #13182013 | C22 | semidirect |
| 23. C4×Dic109 | C22 | semidirect |
| 25. M16×C109 | C22 | semidirect |
| 26. C42×C109 | C22 | semidirect |
| 29. Q8×C109 | C2×C4 | semidirect |
| 31. D4×C109 | C2×C4 | semidirect |
| 42. D436 | C2×C4 | semidirect |
| 52. Dic218 | C2×C4 | semidirect |
| 75. D109 | #104 | direct (N × H) |
| 76. C109 | C2×#104 | semidirect |
| 84. #104 | D109 | direct (N × H) |
| 99. M16 | C2×D109 | semidirect |
| 103. C42 | C2×D109 | semidirect |
| 108. Q8 | C4×D109 | semidirect |
| 115. D4 | C4×D109 | semidirect |