Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 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. C22×C22⋊#6923 | C2 | semidirect |
| 2. C2×#14519836 | C2 | semidirect |
| 3. D61⋊#99 | C2 | direct (N × H) |
| 4. C2×#14519835 | C2 | semidirect |
| 9. C2×C22⋊#6923 | C22 | semidirect |
| 10. C2×C22⋊#6923 | C22 | semidirect |
| 11. #14519836 | C22 | semidirect |
| 12. #14519835 | C22 | semidirect |
| 13. C24×D61 | C4 | semidirect |
| 16. C22×C22⋊D61 | C4 | semidirect |
| 21. C2×D4×D61 | C4 | semidirect |
| 23. C22×C4×D61 | C4 | semidirect |
| 24. C22×D4×C61 | C4 | semidirect |
| 26. C24×C61 | C2×C4 | semidirect |
| 34. C23×D61 | C2×C4 | semidirect |
| 35. C23×D61 | C2×C4 | semidirect |
| 46. C2×D4×C61 | C2×C4 | semidirect |
| 47. C22×C4×C61 | C2×C4 | semidirect |
| 52. C2×C22⋊D61 | C2×C4 | semidirect |
| 53. C2×C22⋊D61 | C2×C4 | semidirect |
| 55. C22×Dic61 | C2×C4 | semidirect |
| 62. C2×D244 | C2×C4 | semidirect |
| 67. C2×C4×D61 | C2×C4 | semidirect |
| 70. C22⋊#6923 | C23 | semidirect |
| 79. C23×C61 | C22×C4 | semidirect |
| 103. C22×D61 | C22×C4 | semidirect |
| 115. C2×C4×C61 | C22×C4 | semidirect |
| 121. C2×Dic61 | C22×C4 | semidirect |
| 155. C2×D61 | #99 | semidirect |
| 168. C2×C61 | C2×#99 | semidirect |
| 174. D61 | C2×#99 | semidirect |
| 180. C61 | C22×#99 | semidirect |
| 191. C22×D4 | #6923 | semidirect |
| 215. C24 | C2×#6923 | semidirect |
| 233. C2×D4 | C2×#6923 | semidirect |
| 242. C22×C4 | C2×#6923 | semidirect |
| 283. C23 | C22×#6923 | semidirect |
| 300. C2×C4 | C22×#6923 | semidirect |
| 347. C2 | D61⋊#99 | direct (N × H) |