Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#381 | C2 |
| hypercenter | #381 | D53 |
| hypocenter | C53 | #2613 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D212 | C2 | semidirect |
| 2. C2×#13133200 | C2 | semidirect |
| 3. C2×#13133187 | C2 | semidirect |
| 4. #16810541 | C2 | semidirect |
| 5. #16810533 | C2 | semidirect |
| 6. #16810478 | C2 | semidirect |
| 7. C53×#381 | C2 | semidirect |
| 12. C22×D212 | C22 | semidirect |
| 16. C2×#11719919 | C22 | semidirect |
| 18. C2×#11719921 | C22 | semidirect |
| 19. C2×#11719921 | C22 | semidirect |
| 20. C2×#11719921 | C22 | semidirect |
| 23. #95×C53 | C22 | semidirect |
| 28. C23×D53 | D4 | semidirect |
| 32. C22×C4×C53 | D4 | semidirect |
| 109. #381 | D53 | semidirect |
| 111. C53 | #2613 | semidirect |
| 127. #95 | C2×D53 | semidirect |
| 145. C22×C4 | D212 | semidirect |