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. C22×#11719913 | C2 | semidirect |
| 2. C2×#13133196 | C2 | semidirect |
| 4. C2×#13133142 | C2 | semidirect |
| 5. C2×#13133139 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C2×C22⋊C8×C53 | C2 | semidirect |
| 56. C2×Dic106 | D4 | semidirect |
| 62. C2×C8×C53 | D4 | semidirect |
| 68. C4⋊Dic53 | D4 | semidirect |
| 77. C23×C53 | SD16 | semidirect |
| 163. C2×C22⋊C8 | D53 | semidirect |
| 165. C53 | #2000 | semidirect |
| 221. C2×C8 | C22⋊D53 | semidirect |
| 242. C23 | #11719913 | semidirect |