Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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×#386 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | #386 | D61 |
| hypocenter | C61 | #2372 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839666 | C2 | semidirect |
| 3. #16839656 | C2 | semidirect |
| 4. #16839650 | C2 | semidirect |
| 6. C22⋊C4×Dic61 | C2 | semidirect |
| 7. C4×C22⋊Dic61 | C2 | semidirect |
| 8. #16839607 | C2 | semidirect |
| 12. #14519764 | C4 | semidirect |
| 50. C2×Dic122 | C2×C4 | semidirect |
| 55. C22⋊Dic61 | C2×C4 | semidirect |
| 56. C22⋊Dic61 | C2×C4 | semidirect |
| 61. C4×Dic61 | C2×C4 | semidirect |
| 137. C61 | #2372 | semidirect |