Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#13182028 | C2 | semidirect |
| 2. C2×D4×D109 | C2 | semidirect |
| 3. #16812723 | C2 | direct (N × H) |
| 4. C2×#13182018 | C2 | semidirect |
| 5. C2×#13182017 | C2 | semidirect |
| 6. C2×#13182014 | C2 | semidirect |
| 7. C2×#13182012 | C2 | semidirect |
| 8. C2×D8×C109 | C2 | semidirect |
| 11. #13182028 | C22 | semidirect |
| 12. C2×Dic218 | C22 | semidirect |
| 17. D4×D109 | C22 | semidirect |
| 20. #13182018 | C22 | semidirect |
| 21. #13182017 | C22 | semidirect |
| 22. #13182014 | C22 | semidirect |
| 23. #13182012 | C22 | semidirect |
| 24. C2×#11724784 | C22 | semidirect |
| 26. C2×D4×C109 | C22 | semidirect |
| 27. D8×C109 | C22 | semidirect |
| 28. C2×C8×C109 | C22 | semidirect |
| 38. D4×C109 | C23 | semidirect |
| 50. Dic218 | C23 | semidirect |
| 51. C8×C109 | C23 | semidirect |
| 52. #11724784 | C23 | semidirect |
| 69. C2×C109 | AGL(1,ℤ/8) | semidirect |
| 73. C109 | C2×AGL(1,ℤ/8) | semidirect |
| 81. C2×D8 | D109 | semidirect |
| 93. C2×D4 | C2×D109 | semidirect |
| 99. D8 | C2×D109 | semidirect |
| 102. C2×C8 | C2×D109 | semidirect |
| 118. D4 | C22×D109 | semidirect |
| 126. C8 | C22×D109 | semidirect |
| 145. C2 | #16812723 | direct (N × H) |