Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 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 | C23 | C22×#6157 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C4⋊C4×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4⋊C4 | #6157 |
| hypocenter | C53 | C2×#433 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811648 | C2 | direct (N × H) |
| 2. C2×#13133284 | C2 | semidirect |
| 3. C2×C4⋊#88324 | C2 | semidirect |
| 6. C2×#13133272 | C2 | semidirect |
| 7. C2×C4×#88324 | C2 | semidirect |
| 13. #13133284 | C22 | semidirect |
| 14. C4⋊#88324 | C22 | semidirect |
| 17. #13133272 | C22 | semidirect |
| 18. C4×#88324 | C22 | semidirect |
| 98. C2×C53 | #433 | semidirect |
| 111. C53 | C2×#433 | semidirect |
| 201. C2 | #16811648 | direct (N × H) |