Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
260 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 260 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, Frattini | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C2×C42 |
| Fitting | C4⋊C8×C53 | C4 |
| hypercenter | C4⋊C8 | #6157 |
| hypocenter | C53 | #1768 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #13133284 | C4 | semidirect |
| 13. C4⋊#88324 | C4 | semidirect |
| 21. C4⋊#88322 | C4 | semidirect |
| 22. #13133146 | C4 | semidirect |
| 23. #13133146 | C4 | semidirect |
| 24. C4⋊C8×C53 | C4 | semidirect |
| 105. C53 | #1768 | semidirect |
| 118. C4⋊C8 | #6157 | semidirect |