Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D53 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. C22×#11719922 | C2 | semidirect |
| 4. C2×#13133192 | C2 | semidirect |
| 5. #16810758 | C2 | direct (N × H) |
| 6. C2×#13133137 | C2 | semidirect |
| 7. C2×#13133129 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 12. C22×D212 | C22 | semidirect |
| 17. C2×D4×D53 | C22 | semidirect |
| 20. C2×D424 | C22 | semidirect |
| 22. C2×#11719922 | C22 | semidirect |
| 23. C22×#88322 | C22 | semidirect |
| 25. #13133192 | C22 | semidirect |
| 27. #13133137 | C22 | semidirect |
| 28. #13133129 | C22 | semidirect |
| 30. C22×C8×C53 | C22 | semidirect |
| 31. C2×C4⋊C4×C53 | C22 | semidirect |
| 32. #102×C53 | C22 | semidirect |
| 43. C2×D4×C53 | D4 | semidirect |
| 60. C2×D212 | D4 | semidirect |
| 62. C2×D212 | C23 | semidirect |
| 68. C2×C8×C53 | C23 | semidirect |
| 70. C4⋊C4×C53 | C23 | semidirect |
| 74. C2×#88322 | C23 | semidirect |
| 95. C22×D53 | D8 | semidirect |
| 99. D4×C53 | C2×D4 | semidirect |
| 115. D212 | C2×D4 | semidirect |
| 141. C2×D53 | C2×D8 | semidirect |
| 149. C2×C53 | #447 | semidirect |
| 162. C2×#102 | D53 | semidirect |
| 164. C53 | C2×#447 | semidirect |
| 181. C22×C8 | C2×D53 | semidirect |
| 184. C2×C4⋊C4 | C2×D53 | semidirect |
| 187. #102 | C2×D53 | semidirect |
| 214. C2×D4 | D212 | semidirect |
| 228. C2×C8 | C22×D53 | semidirect |
| 230. C4⋊C4 | C22×D53 | semidirect |
| 263. D4 | C2×D212 | semidirect |
| 307. C2 | #16810758 | direct (N × H) |