Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×#13083574 | C2 | semidirect |
| 2. #15668038 | C2 | direct (N × H) |
| 3. C2×#13083562 | C2 | semidirect |
| 4. C2×#13083559 | C2 | semidirect |
| 5. C2×#13083558 | C2 | semidirect |
| 6. C22×D4×C89 | C2 | semidirect |
| 8. #13083574 | C22 | semidirect |
| 9. C2×Dic178 | C22 | semidirect |
| 10. C2×D356 | C22 | semidirect |
| 13. #13083562 | C22 | semidirect |
| 14. #13083559 | C22 | semidirect |
| 15. #13083558 | C22 | semidirect |
| 16. C2×#10623494 | C22 | semidirect |
| 21. C2×D4×C89 | C22 | semidirect |
| 38. D356 | C23 | semidirect |
| 41. Dic178 | C23 | semidirect |
| 42. #10623494 | C23 | semidirect |
| 57. C2×C89 | AGL(1,ℤ/8) | semidirect |
| 60. C89 | C2×AGL(1,ℤ/8) | semidirect |
| 63. C22×D4 | D89 | semidirect |
| 77. C2×D4 | C2×D89 | semidirect |
| 119. C2 | #15668038 | direct (N × H) |