Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1232 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C23×D4×C53 | C2 |
| hypercenter | C23×D4 | D53 |
| hypocenter | C53 | #2408 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133188 | C2 | semidirect |
| 2. C2×#13133186 | C2 | semidirect |
| 3. C2×C4×C22⋊D53 | C2 | semidirect |
| 4. #16810537 | C2 | semidirect |
| 5. #16810531 | C2 | semidirect |
| 6. #16810526 | C2 | semidirect |
| 7. #16810483 | C2 | semidirect |
| 8. #16810479 | C2 | semidirect |
| 9. C23×D4×C53 | C2 | semidirect |
| 11. C22×C22⋊D53 | C22 | semidirect |
| 12. C22×C4×D53 | C22 | semidirect |
| 16. C2×C4⋊Dic53 | C22 | semidirect |
| 17. C2×#11719919 | C22 | semidirect |
| 20. C2×C22⋊Dic53 | C22 | semidirect |
| 21. C2×C22⋊Dic53 | C22 | semidirect |
| 22. C2×C22⋊Dic53 | C22 | semidirect |
| 23. C2×#11719921 | C22 | semidirect |
| 24. C2×C4×Dic53 | C22 | semidirect |
| 25. #13133124 | C22 | semidirect |
| 45. C2×D4×C53 | D4 | semidirect |
| 47. C22×C4×C53 | D4 | semidirect |
| 55. C2×C22⋊D53 | D4 | semidirect |
| 93. C22×D53 | C2×D4 | semidirect |
| 112. C2×Dic53 | C2×D4 | semidirect |
| 126. C22×C53 | #121 | semidirect |
| 138. C4×C53 | #120 | semidirect |
| 152. C23×D4 | D53 | semidirect |
| 161. C53 | #2408 | semidirect |
| 203. C2×D4 | C22⋊D53 | semidirect |
| 211. C22×C4 | C22⋊D53 | semidirect |
| 283. C22 | #13133188 | semidirect |
| 294. C4 | #13133186 | semidirect |