Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 | #97×C53 | C4 |
| hypercenter | #97 | #6157 |
| hypocenter | C53 | #1771 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #13133284 | C4 | semidirect |
| 14. C4⋊#88324 | C4 | semidirect |
| 21. #13133128 | C4 | semidirect |
| 22. #13133127 | C4 | semidirect |
| 23. #13133127 | C4 | semidirect |
| 24. #97×C53 | C4 | semidirect |
| 75. C8×C53 | C4⋊C4 | semidirect |
| 77. #88322 | C4⋊C4 | semidirect |
| 106. C53 | #1771 | semidirect |
| 121. #97 | #6157 | semidirect |
| 176. C8 | C4⋊#6157 | semidirect |