Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | #117×C61 | C4 |
| hypercenter | #117 | #6923 |
| hypocenter | C61 | #2296 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16840713 | C2 | semidirect |
| 5. C4×C4⋊#6923 | C2 | semidirect |
| 18. #14519736 | C4 | semidirect |
| 19. #14519735 | C4 | semidirect |
| 20. #14519734 | C4 | semidirect |
| 21. #14519733 | C4 | semidirect |
| 25. #117×C61 | C4 | semidirect |
| 46. C4⋊C4×C61 | C2×C4 | semidirect |
| 48. C42×C61 | C2×C4 | semidirect |
| 51. C4⋊Dic61 | C2×C4 | semidirect |
| 52. #11758196 | C2×C4 | semidirect |
| 53. C4×Dic61 | C2×C4 | semidirect |
| 54. C4×Dic61 | C2×C4 | semidirect |
| 67. C2×C4×C61 | C4⋊C4 | semidirect |
| 71. C2×Dic61 | C4⋊C4 | semidirect |
| 76. C4×D61 | C4⋊C4 | semidirect |
| 77. C4×D61 | C4⋊C4 | semidirect |
| 113. C61 | #2296 | semidirect |
| 121. #117 | #6923 | semidirect |
| 151. C4⋊C4 | C2×#6923 | semidirect |
| 161. C42 | C2×#6923 | semidirect |
| 185. C2×C4 | C4⋊#6923 | semidirect |