Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C4⋊#6923 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C4 | C23×#6923 |
| Fitting | #131×C61 | C4 |
| socle | C2×C61 | C22×C4⋊C4 |
| hypercenter | #131 | #6923 |
| hypocenter | C61 | #2912 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840773 | C2 | semidirect |
| 3. #16840772 | C2 | semidirect |
| 4. C2×#14519845 | C2 | semidirect |
| 15. #14519785 | C4 | semidirect |
| 16. #14519784 | C4 | semidirect |
| 17. #14519783 | C4 | semidirect |
| 20. #131×C61 | C4 | semidirect |
| 34. M16×C61 | C2×C4 | semidirect |
| 35. C2×C8×C61 | C2×C4 | semidirect |
| 36. #11758194 | C2×C4 | semidirect |
| 37. C2×#92418 | C2×C4 | semidirect |
| 38. #11758189 | C2×C4 | semidirect |
| 39. C8×D61 | C2×C4 | semidirect |
| 40. C8×D61 | C2×C4 | semidirect |
| 82. C61 | #2912 | semidirect |
| 87. #131 | #6923 | semidirect |
| 108. M16 | C2×#6923 | semidirect |
| 114. C2×C8 | C2×#6923 | semidirect |