Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 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. C23×#10587739 | C2 | semidirect |
| 2. D4×#10587739 | C2 | direct (N × H) |
| 3. C2×C4⋊#10587739 | C2 | semidirect |
| 4. C2×C22⋊#10587739 | C2 | semidirect |
| 5. C2×C4×#10587739 | C2 | semidirect |
| 11. C22×#10587739 | C22 | semidirect |
| 12. C4⋊#10587739 | C22 | semidirect |
| 13. C22⋊#10587739 | C22 | semidirect |
| 14. C4×#10587739 | C22 | semidirect |
| 16. C2×D548 | C4 | semidirect |
| 17. C2×C22⋊D137 | C4 | semidirect |
| 18. D4×D137 | C4 | semidirect |
| 21. C2×D4×C137 | C4 | semidirect |
| 25. C2×#10587739 | D4 | direct (N × H) |
| 31. C22×D137 | C2×C4 | semidirect |
| 32. C22×D137 | C2×C4 | semidirect |
| 35. D548 | C2×C4 | semidirect |
| 36. C22⋊D137 | C2×C4 | semidirect |
| 37. C2×Dic137 | C2×C4 | semidirect |
| 38. C4×D137 | C2×C4 | semidirect |
| 40. C23×C137 | C2×C4 | semidirect |
| 41. D4×C137 | C2×C4 | semidirect |
| 42. C2×C4×C137 | C2×C4 | semidirect |
| 45. C22×C137 | C22×C4 | semidirect |
| 51. C2×D137 | C22×C4 | semidirect |
| 57. #10587739 | C2×D4 | direct (N × H) |
| 58. C4×C137 | C22×C4 | semidirect |
| 59. Dic137 | C22×C4 | semidirect |
| 61. C2×C137 | C4×D4 | semidirect |
| 64. D137 | C4×D4 | semidirect |
| 67. C137 | C2×C4×D4 | semidirect |
| 80. C2×D4 | #10587739 | direct (N × H) |
| 96. C23 | C2×#10587739 | semidirect |
| 99. D4 | C2×#10587739 | direct (N × H) |
| 110. C2×C4 | C2×#10587739 | semidirect |
| 122. C22 | C22×#10587739 | semidirect |
| 127. C4 | C22×#10587739 | semidirect |
| 133. C2 | D4×#10587739 | direct (N × H) |