Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
272 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C4⋊#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | #97×C61 | C4 |
| socle | C22×C61 | C2×C4⋊C4 |
| hypercenter | #97 | #6923 |
| hypocenter | C61 | #1776 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #14519846 | C4 | semidirect |
| 10. #14519845 | C4 | semidirect |
| 15. #14519688 | C4 | semidirect |
| 16. #14519687 | C4 | semidirect |
| 17. #14519687 | C4 | semidirect |
| 18. #97×C61 | C4 | semidirect |
| 57. C8×C61 | C42 | semidirect |
| 59. #92418 | C42 | semidirect |
| 84. C61 | #1776 | semidirect |
| 96. #97 | #6923 | semidirect |
| 138. C8 | C4×#6923 | semidirect |