Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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 | #2298 |
| 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 |
|---|---|---|
| 2. #16811572 | C2 | semidirect |
| 3. C4×C4⋊#6157 | C2 | semidirect |
| 5. #16811559 | C2 | semidirect |
| 6. C42×#6157 | C2 | semidirect |
| 17. #13133176 | C4 | semidirect |
| 18. #13133175 | C4 | semidirect |
| 19. #13133174 | C4 | semidirect |
| 20. #13133174 | C4 | semidirect |
| 21. #13133173 | C4 | semidirect |
| 26. #117×C53 | C4 | semidirect |
| 116. C53 | #2298 | semidirect |
| 123. #117 | #6157 | semidirect |