Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#442 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #442 | D53 |
| hypocenter | C53 | #2952 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811102 | C2 | semidirect |
| 3. #16810735 | C2 | semidirect |
| 4. #16810731 | C2 | semidirect |
| 5. #16810729 | C2 | semidirect |
| 6. #16810714 | C2 | semidirect |
| 7. C4×#11719923 | C2 | semidirect |
| 8. #106×D53 | C2 | semidirect |
| 9. #16810621 | C2 | semidirect |
| 10. #16810580 | C2 | semidirect |
| 11. C53×#442 | C2 | semidirect |
| 13. #13133236 | C4 | semidirect |
| 46. #11719947 | C2×C4 | semidirect |
| 50. D8×C53 | C2×C4 | semidirect |
| 57. #11719923 | C2×C4 | semidirect |
| 69. Dic212 | C2×C4 | semidirect |
| 71. C8×D53 | C2×C4 | semidirect |
| 118. #442 | D53 | semidirect |
| 126. C53 | #2952 | semidirect |
| 167. D8 | C4×D53 | semidirect |