Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | #106×C61 | C4 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #106 | #6923 |
| hypocenter | C61 | #1776 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #106 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #14519846 | C4 | semidirect |
| 11. #14519831 | C4 | semidirect |
| 15. #14519709 | C4 | semidirect |
| 16. #14519708 | C4 | semidirect |
| 17. #106×C61 | C4 | semidirect |
| 55. C8×C61 | C42 | semidirect |
| 56. #92418 | C42 | semidirect |
| 81. C61 | #1776 | semidirect |
| 91. #106 | #6923 | semidirect |
| 132. C8 | C4×#6923 | semidirect |