Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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. #16811641 | C2 | semidirect |
| 2. D53⋊(C4⋊C8) | C2 | semidirect |
| 3. Q8⋊#88324 | C2 | semidirect |
| 4. #16811471 | C2 | semidirect |
| 25. #11719949 | C8 | semidirect |
| 54. Q8×C53 | C2×C8 | semidirect |
| 66. D212 | C2×C8 | semidirect |
| 107. C53 | #1477 | semidirect |
| 156. Q8 | D53⋊C8 | semidirect |