Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 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×#11719924 | C2 | semidirect |
| 3. C2×#13133139 | C2 | semidirect |
| 4. C2×#13133138 | C2 | semidirect |
| 5. #16810530 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C22×SD16×C53 | C2 | semidirect |
| 34. C2×Q8×C53 | D4 | semidirect |
| 57. C2×C8×C53 | D4 | semidirect |
| 65. C2×#88322 | D4 | semidirect |
| 99. C2×Dic53 | SD16 | semidirect |
| 137. C22×SD16 | D53 | semidirect |
| 143. C53 | #2014 | semidirect |
| 170. C2×Q8 | C22⋊D53 | semidirect |
| 197. C2×C8 | C22⋊D53 | semidirect |