Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#13133193 | C2 | semidirect |
| 3. C2×#13133141 | C2 | semidirect |
| 4. C2×#13133138 | C2 | semidirect |
| 5. C2×#13133129 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C22×SD16×C53 | C2 | semidirect |
| 36. C2×Q8×C53 | D4 | semidirect |
| 60. C2×C8×C53 | D4 | semidirect |
| 66. C4⋊Dic53 | D4 | semidirect |
| 85. C22×D53 | SD16 | semidirect |
| 158. C22×SD16 | D53 | semidirect |
| 165. C53 | #2000 | semidirect |
| 194. C2×Q8 | C22⋊D53 | semidirect |
| 221. C2×C8 | C22⋊D53 | semidirect |