Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 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 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#543 | C2 |
| hypercenter | #543 | D61 |
| hypocenter | C61 | C2×#543 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840388 | C2 | semidirect |
| 2. #16840387 | C2 | semidirect |
| 3. C22⋊Q8×D61 | C2 | semidirect |
| 5. C61×#543 | C2 | semidirect |
| 7. C2×Q8×D61 | C22 | semidirect |
| 9. #14519757 | C22 | semidirect |
| 10. #14519756 | C22 | semidirect |
| 11. #14519755 | C22 | semidirect |
| 12. #14519754 | C22 | semidirect |
| 13. #14519753 | C22 | semidirect |
| 14. C4⋊C4×D61 | C22 | semidirect |
| 19. C22⋊Q8×C61 | C22 | semidirect |
| 23. C23×D61 | Q8 | semidirect |
| 26. C2×Q8×C61 | C23 | semidirect |
| 33. C2×Dic122 | C23 | semidirect |
| 34. C4⋊C4×C61 | C23 | semidirect |
| 38. C4⋊Dic61 | C23 | semidirect |
| 39. #11758196 | C23 | semidirect |
| 41. C23×C61 | C2×Q8 | semidirect |
| 47. C22×D61 | C2×Q8 | semidirect |
| 75. D61 | #543 | direct (N × H) |
| 78. #543 | D61 | direct (N × H) |
| 81. C61 | C2×#543 | semidirect |
| 90. C22⋊Q8 | C2×D61 | semidirect |
| 104. C2×Q8 | C22×D61 | semidirect |
| 112. C4⋊C4 | C22×D61 | semidirect |
| 124. C23 | Q8×D61 | semidirect |