Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13133189 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#421 | C2 |
| socle | C2×C53 | #390 |
| hypercenter | #421 | D53 |
| hypocenter | C53 | #1976 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810659 | C2 | semidirect |
| 3. #16810639 | C2 | semidirect |
| 4. #16810597 | C2 | semidirect |
| 5. #16810596 | C2 | semidirect |
| 6. #16810581 | C2 | semidirect |
| 7. C53×#421 | C2 | semidirect |
| 13. C2×#11719925 | C4 | semidirect |
| 14. C2×#11719923 | C4 | semidirect |
| 15. C2×#11719924 | C4 | semidirect |
| 16. C2×#11719922 | C4 | semidirect |
| 136. #421 | D53 | semidirect |
| 140. C53 | #1976 | semidirect |