Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811593 | C2 | semidirect |
| 2. C2×C22⋊#88324 | C2 | semidirect |
| 3. #16811467 | C2 | semidirect |
| 4. #16811466 | C2 | semidirect |
| 129. C53 | #1471 | semidirect |