Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C4×D4×C61 | C4 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | #2319 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840713 | C2 | semidirect |
| 3. #16840712 | C2 | semidirect |
| 4. #16840705 | C2 | semidirect |
| 5. #16840704 | C2 | semidirect |
| 6. C4×C4⋊#6923 | C2 | semidirect |
| 7. #16840698 | C2 | semidirect |
| 22. C4×D244 | C4 | semidirect |
| 23. D4×Dic61 | C4 | semidirect |
| 24. #14519739 | C4 | semidirect |
| 25. C4×C22⋊D61 | C4 | semidirect |
| 26. #14519737 | C4 | semidirect |
| 30. C4×D4×C61 | C4 | semidirect |
| 141. C61 | #2319 | semidirect |
| 149. C4×D4 | #6923 | semidirect |