Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#11719922 | C2 | semidirect |
| 2. C2×#13133213 | C2 | semidirect |
| 3. C2×#13133139 | C2 | semidirect |
| 4. C2×#13133138 | C2 | semidirect |
| 5. #16810526 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C22×D8×C53 | C2 | semidirect |
| 41. C2×D4×C53 | D4 | semidirect |
| 57. C2×C8×C53 | D4 | semidirect |
| 66. C2×#88322 | D4 | semidirect |
| 102. C2×Dic53 | D8 | semidirect |
| 145. C22×D8 | D53 | semidirect |
| 151. C53 | #2011 | semidirect |
| 194. C2×D4 | C22⋊D53 | semidirect |
| 205. C2×C8 | C22⋊D53 | semidirect |