Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #103×C61 | C4 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #103 | #6923 |
| hypocenter | C61 | #1764 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #103 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16840727 | C2 | semidirect |
| 4. C2×C8×#6923 | C2 | semidirect |
| 5. #16840638 | C2 | semidirect |
| 6. #16840632 | C2 | semidirect |
| 9. #14519865 | C4 | semidirect |
| 16. #14519842 | C4 | semidirect |
| 23. #14519701 | C4 | semidirect |
| 24. #14519699 | C4 | semidirect |
| 25. #14519697 | C4 | semidirect |
| 26. #103×C61 | C4 | semidirect |
| 117. C61 | #1764 | semidirect |
| 131. #103 | #6923 | semidirect |