Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 58 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. #16811658 | C2 | semidirect |
| 2. #16811486 | C2 | semidirect |
| 3. D4⋊#88324 | C2 | semidirect |
| 4. C8×#88324 | C2 | semidirect |
| 41. #88324 | D8 | semidirect |
| 42. C8×C53 | M16 | semidirect |
| 64. C53 | #1589 | semidirect |
| 102. C8 | #11719940 | semidirect |