Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D244 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#407 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #407 | D61 |
| hypocenter | C61 | #3192 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519751 | C2 | semidirect |
| 2. #16840081 | C2 | semidirect |
| 3. #16840015 | C2 | semidirect |
| 4. #16839898 | C2 | semidirect |
| 5. C61×#407 | C2 | semidirect |
| 6. C22×D244 | C22 | semidirect |
| 8. C2×D488 | C22 | semidirect |
| 12. #14519751 | C22 | semidirect |
| 13. C2×C4⋊Dic61 | C22 | semidirect |
| 15. #14519709 | C22 | semidirect |
| 16. #14519699 | C22 | semidirect |
| 18. C2×M16×C61 | C22 | semidirect |
| 19. C22⋊C8×C61 | C22 | semidirect |
| 88. #407 | D61 | semidirect |
| 89. C61 | #3192 | semidirect |
| 94. C2×M16 | C2×D61 | semidirect |
| 103. C22⋊C8 | C2×D61 | semidirect |