Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11719923 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. C2×#13133205 | C2 | semidirect |
| 4. #16811010 | C2 | direct (N × H) |
| 5. C2×#13133128 | C2 | semidirect |
| 6. C2×#127×C53 | C2 | semidirect |
| 10. C2×#11719923 | C22 | semidirect |
| 12. C2×#11719922 | C22 | semidirect |
| 15. #13133205 | C22 | semidirect |
| 17. #13133128 | C22 | semidirect |
| 21. #127×C53 | C22 | semidirect |
| 45. C2×#88322 | D4 | semidirect |
| 69. #88322 | C2×D4 | semidirect |
| 85. C2×C53 | #496 | semidirect |
| 91. C2×#127 | D53 | semidirect |
| 95. C53 | C2×#496 | semidirect |
| 106. #127 | C2×D53 | semidirect |
| 174. C2 | #16811010 | direct (N × H) |