Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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, socle | C23×C61 | C24 |
| Fitting | C61×#379 | C2 |
| hypercenter | #379 | D61 |
| hypocenter | C61 | #2848 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519754 | C2 | semidirect |
| 3. #16839637 | C2 | semidirect |
| 4. #16839634 | C2 | semidirect |
| 5. #16839620 | C2 | semidirect |
| 8. C22×Dic122 | C22 | semidirect |
| 13. C2×C4⋊Dic61 | C22 | semidirect |
| 14. C2×#11758196 | C22 | semidirect |
| 15. C2×#11758196 | C22 | semidirect |
| 18. #14519684 | C22 | semidirect |
| 24. C24×C61 | Q8 | semidirect |
| 71. C22×C61 | C22⋊Q8 | semidirect |
| 93. C61 | #2848 | semidirect |
| 110. C24 | Dic122 | semidirect |
| 157. C22 | #14519754 | semidirect |