Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 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 | C22⋊C8×C53 | C4 |
| hypercenter | C22⋊C8 | #6157 |
| hypocenter | C53 | #1750 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13133271 | C2 | semidirect |
| 4. C2×C8×#6157 | C2 | semidirect |
| 5. (C2×#6157)⋊C8 | C2 | semidirect |
| 6. (C2×#6157)⋊C8 | C2 | semidirect |
| 16. #13133274 | C4 | semidirect |
| 17. C22⋊#88324 | C4 | semidirect |
| 23. C22⋊#88322 | C4 | semidirect |
| 24. #13133129 | C4 | semidirect |
| 25. #13133129 | C4 | semidirect |
| 26. C22⋊C8×C53 | C4 | semidirect |
| 133. C53 | #1750 | semidirect |
| 150. C22⋊C8 | #6157 | semidirect |