Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 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×#13133141 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×C22⋊Q8×C53 | C2 | semidirect |
| 36. C2×Q8×C53 | D4 | semidirect |
| 59. C4⋊C4×C53 | D4 | semidirect |
| 70. C2×#88322 | D4 | semidirect |
| 77. C23×C53 | SD16 | semidirect |
| 159. C2×C22⋊Q8 | D53 | semidirect |
| 165. C53 | #2000 | semidirect |
| 194. C2×Q8 | C22⋊D53 | semidirect |
| 226. C4⋊C4 | C22⋊D53 | semidirect |
| 242. C23 | #11719924 | semidirect |