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×#13133285 | 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 |
| 63. C8×C53 | C22⋊C4 | semidirect |
| 65. #88322 | C22⋊C4 | semidirect |
| 68. C22×C53 | #106 | semidirect |
| 73. C2×D53 | #106 | semidirect |
| 94. C53 | #1807 | semidirect |
| 102. C22×C8 | #6157 | semidirect |
| 155. C8 | C22⋊#6157 | semidirect |
| 165. C22 | #13133285 | semidirect |