Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519749 |
| commutator | C2×C4×C61 | C22×C4 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#421 | C2 |
| socle | C2×C61 | #388 |
| hypercenter | #421 | D61 |
| hypocenter | C61 | #1932 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16839810 | C2 | semidirect |
| 4. M16×Dic61 | C2 | semidirect |
| 5. #16839532 | C2 | semidirect |
| 6. #16839521 | C2 | semidirect |
| 15. #14519696 | C4 | semidirect |
| 16. #14519694 | C4 | semidirect |
| 103. C61 | #1932 | semidirect |