Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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×#13133286 | C2 | semidirect |
| 3. #16811497 | C2 | semidirect |
| 10. C22×#88322 | C4 | semidirect |
| 12. C2×C8×D53 | C4 | semidirect |
| 13. C2×C8×D53 | C4 | semidirect |
| 16. C22×C8×C53 | C4 | semidirect |
| 64. C8×C53 | C22⋊C4 | semidirect |
| 66. #88322 | C22⋊C4 | semidirect |
| 69. C22×C53 | #107 | semidirect |
| 75. C2×D53 | #107 | semidirect |
| 98. C53 | #1808 | semidirect |
| 106. C22×C8 | #6157 | semidirect |
| 160. C8 | C22⋊#6157 | semidirect |
| 172. C22 | #13133286 | semidirect |