Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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. #16812778 | C2 | direct (N × H) |
| 2. C2×C4⋊#89137 | C2 | semidirect |
| 4. C2×C4×#89137 | C2 | semidirect |
| 7. C4⋊#89137 | C22 | semidirect |
| 9. C4×#89137 | C22 | semidirect |
| 11. C22×Dic109 | C4 | semidirect |
| 12. C2×C4×D109 | C4 | semidirect |
| 13. C2×C4×D109 | C4 | semidirect |
| 14. C2×C4×D109 | C4 | semidirect |
| 18. C22×C4×C109 | C4 | semidirect |
| 29. C2×C4×C109 | C2×C4 | semidirect |
| 32. C2×Dic109 | C2×C4 | semidirect |
| 35. C4×D109 | C2×C4 | semidirect |
| 36. C4×D109 | C2×C4 | semidirect |
| 55. C2×C109 | #117 | semidirect |
| 58. D109 | #117 | semidirect |
| 60. C109 | C2×#117 | semidirect |
| 76. C22×C4 | #89137 | semidirect |
| 99. C2×C4 | C2×#89137 | semidirect |
| 119. C2 | #16812778 | direct (N × H) |