Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C61×#390 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | #390 | D61 |
| hypocenter | C61 | C4×#124 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519742 | C2 | semidirect |
| 4. #16839668 | C2 | semidirect |
| 5. #16839650 | C2 | semidirect |
| 6. #16839627 | C2 | semidirect |
| 7. C22⋊C4×Dic61 | C2 | semidirect |
| 8. C42×Dic61 | C2 | semidirect |
| 12. #14519764 | C4 | semidirect |
| 46. C2×Dic122 | C2×C4 | semidirect |
| 51. C22⋊Dic61 | C2×C4 | semidirect |
| 57. C4×Dic61 | C2×C4 | semidirect |
| 105. Dic61 | #124 | semidirect |
| 122. C61 | C4×#124 | semidirect |