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×#13182030 | C2 | semidirect |
| 2. C2×D4×D109 | C2 | semidirect |
| 3. #16812726 | C2 | direct (N × H) |
| 4. C2×#13182016 | C2 | semidirect |
| 5. C2×D872 | C2 | semidirect |
| 6. C2×#13182014 | C2 | semidirect |
| 7. C2×#13182012 | C2 | semidirect |
| 8. C2×SD16×C109 | C2 | semidirect |
| 11. #13182030 | C22 | semidirect |
| 14. C2×D436 | C22 | semidirect |
| 17. D4×D109 | C22 | semidirect |
| 20. #13182016 | C22 | semidirect |
| 21. D872 | C22 | semidirect |
| 22. #13182014 | C22 | semidirect |
| 23. #13182012 | C22 | semidirect |
| 24. C2×#11724784 | C22 | semidirect |
| 25. C2×Q8×C109 | C22 | semidirect |
| 27. SD16×C109 | C22 | semidirect |
| 28. C2×C8×C109 | C22 | semidirect |
| 36. Q8×C109 | C23 | semidirect |
| 47. D436 | C23 | semidirect |
| 51. C8×C109 | C23 | semidirect |
| 52. #11724784 | C23 | semidirect |
| 68. C2×C109 | AGL(1,ℤ/8) | semidirect |
| 73. C109 | C2×AGL(1,ℤ/8) | semidirect |
| 79. C2×SD16 | D109 | semidirect |
| 86. C2×Q8 | C2×D109 | semidirect |
| 97. SD16 | C2×D109 | semidirect |
| 102. C2×C8 | C2×D109 | semidirect |
| 110. Q8 | C22×D109 | semidirect |
| 126. C8 | C22×D109 | semidirect |
| 145. C2 | #16812726 | direct (N × H) |