Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×#13182039 | C2 | semidirect |
| 2. C2×C4×#89137 | C2 | semidirect |
| 3. #16812764 | C2 | direct (N × H) |
| 7. #13182039 | C22 | semidirect |
| 10. C4×#89137 | C22 | semidirect |
| 13. #13182030 | C4 | semidirect |
| 16. C2×D436 | C4 | semidirect |
| 19. C2×Q8×C109 | C4 | semidirect |
| 25. Q8×C109 | C2×C4 | semidirect |
| 32. D436 | C2×C4 | semidirect |
| 52. C2×C109 | #104 | semidirect |
| 57. C109 | C2×#104 | semidirect |
| 67. C2×Q8 | #89137 | semidirect |
| 81. Q8 | C2×#89137 | semidirect |
| 113. C2 | #16812764 | direct (N × H) |