Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C22⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C4×C22⋊C4 | D61 |
| hypocenter | C61 | #2312 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839653 | C2 | semidirect |
| 3. #16839651 | C2 | semidirect |
| 4. #16839620 | C2 | semidirect |
| 6. C4×C22⋊Dic61 | C2 | semidirect |
| 7. C4×C22⋊C4×C61 | C2 | semidirect |
| 10. C2×#11758196 | C22 | semidirect |
| 12. C2×#11758198 | C4 | semidirect |
| 17. C2×C4×Dic61 | C22 | semidirect |
| 18. #14519684 | C22 | semidirect |
| 19. #14519684 | C22 | semidirect |
| 22. C2×C42×C61 | C22 | semidirect |
| 23. #95×C61 | C22 | semidirect |
| 106. C4×C22⋊C4 | D61 | semidirect |
| 107. C61 | #2312 | semidirect |
| 120. C2×C42 | C2×D61 | semidirect |
| 123. #95 | C2×D61 | semidirect |