Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Frattini | C22 | C23×#6157 |
| Fitting | #117×C53 | C4 |
| hypercenter | #117 | #6157 |
| hypocenter | C53 | C2×#424 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16811630 | C2 | semidirect |
| 4. #16811629 | C2 | semidirect |
| 5. D53⋊(C4⋊C8) | C2 | semidirect |
| 15. #13133284 | C22 | semidirect |
| 16. C4⋊#88324 | C22 | semidirect |
| 96. D53 | #424 | semidirect |
| 103. C53 | C2×#424 | semidirect |