Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×#6157 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | #103×C53 | C4 |
| socle | C22×C53 | C4×D4 |
| hypercenter | #103 | #6157 |
| hypocenter | C53 | #1763 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #103 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. Q8×#6157 | C4 | semidirect |
| 17. #13133280 | C4 | semidirect |
| 23. #13133142 | C4 | semidirect |
| 24. #13133141 | C4 | semidirect |
| 25. #13133140 | C4 | semidirect |
| 26. #103×C53 | C4 | semidirect |
| 74. Q8×C53 | C42 | semidirect |
| 92. Dic106 | C42 | semidirect |
| 130. C53 | #1763 | semidirect |
| 147. #103 | #6157 | semidirect |
| 189. Q8 | C4×#6157 | semidirect |