Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D53 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#473 | C2 |
| socle | C2×C53 | C2×#121 |
| hypercenter | #473 | D53 |
| hypocenter | C53 | #3067 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811422 | C2 | semidirect |
| 2. C2×#13133240 | C2 | semidirect |
| 3. #131×D53 | C2 | semidirect |
| 4. #16810895 | C2 | semidirect |
| 5. #16810894 | C2 | semidirect |
| 6. #16810893 | C2 | semidirect |
| 7. #16810889 | C2 | semidirect |
| 8. #16810888 | C2 | semidirect |
| 9. #108×D53 | C2 | semidirect |
| 10. #16810606 | C2 | semidirect |
| 11. C53×#473 | C2 | semidirect |
| 25. C2×#11719924 | C22 | semidirect |
| 26. C2×D424 | C22 | semidirect |
| 37. #13133153 | C22 | semidirect |
| 38. #13133152 | C22 | semidirect |
| 39. #13133136 | C22 | semidirect |
| 40. #13133133 | C22 | semidirect |
| 41. #13133133 | C22 | semidirect |
| 43. C2×Q16×C53 | C22 | semidirect |
| 45. #108×C53 | C22 | semidirect |
| 46. #101×C53 | C22 | semidirect |
| 171. #473 | D53 | semidirect |
| 178. C53 | #3067 | semidirect |
| 193. C2×Q16 | C2×D53 | semidirect |
| 209. #108 | C2×D53 | semidirect |
| 211. #101 | C2×D53 | semidirect |