Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C43 |
| Fitting | #97×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | #97 | #6923 |
| hypocenter | C61 | C4×#97 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #14519832 | C4 | semidirect |
| 11. #14519831 | C4 | semidirect |
| 12. C8×#6923 | C4 | semidirect |
| 15. #14519688 | C4 | semidirect |
| 16. #14519687 | C4 | semidirect |
| 17. #97×C61 | C4 | semidirect |
| 47. #92420 | C42 | semidirect |
| 48. C8×C61 | C42 | semidirect |
| 49. #92418 | C42 | semidirect |
| 55. #6923 | #97 | direct (N × H) |
| 70. C61 | C4×#97 | semidirect |
| 81. #97 | #6923 | direct (N × H) |
| 114. C8 | C4×#6923 | semidirect |