Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. M16×#6923 | C2 | semidirect |
| 4. C42×#6923 | C2 | semidirect |
| 5. #16840634 | C2 | semidirect |
| 6. #16840633 | C2 | semidirect |
| 9. Q8×#6923 | C4 | semidirect |
| 11. D4×#6923 | C4 | semidirect |
| 18. #14519842 | C4 | semidirect |
| 19. #14519841 | C4 | semidirect |
| 25. #14519705 | C4 | semidirect |
| 26. #14519704 | C4 | semidirect |
| 27. #14519703 | C4 | semidirect |
| 28. #104×C61 | C4 | semidirect |
| 54. C4×#6923 | C2×C4 | semidirect |
| 57. #11758213 | C2×C4 | semidirect |
| 59. M16×C61 | C2×C4 | semidirect |
| 60. C42×C61 | C2×C4 | semidirect |
| 62. C4×Dic61 | C2×C4 | semidirect |
| 63. #11758194 | C2×C4 | semidirect |
| 75. Q8×C61 | C42 | semidirect |
| 77. D4×C61 | C42 | semidirect |
| 88. D244 | C42 | semidirect |
| 98. Dic122 | C42 | semidirect |
| 112. #6923 | #104 | direct (N × H) |
| 135. C61 | C4×#104 | semidirect |
| 154. #104 | #6923 | direct (N × H) |
| 176. M16 | C2×#6923 | semidirect |
| 193. C42 | C2×#6923 | semidirect |
| 198. Q8 | C4×#6923 | semidirect |
| 205. D4 | C4×#6923 | semidirect |