Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator | C2×C61 | C24×C4 |
| Fitting | C61×#519 | C2 |
| socle | C22×C61 | C25 |
| hypercenter | #519 | D61 |
| hypocenter | C61 | C2×#519 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840240 | C2 | semidirect |
| 3. #16840239 | C2 | semidirect |
| 4. #16840238 | C2 | semidirect |
| 5. C4×Q8×D61 | C2 | semidirect |
| 7. C61×#519 | C2 | semidirect |
| 9. C2×Q8×D61 | C4 | semidirect |
| 13. Q8×Dic61 | C22 | semidirect |
| 14. C4×Dic122 | C22 | semidirect |
| 15. #14519742 | C22 | semidirect |
| 24. C4×Q8×C61 | C22 | semidirect |
| 27. C2×Q8×C61 | C2×C4 | semidirect |
| 32. Q8×D61 | C2×C4 | semidirect |
| 37. C2×Dic122 | C2×C4 | semidirect |
| 81. D61 | #519 | direct (N × H) |
| 86. #519 | D61 | direct (N × H) |
| 89. C61 | C2×#519 | semidirect |
| 99. C4×Q8 | C2×D61 | semidirect |
| 113. C2×Q8 | C4×D61 | semidirect |