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×#11719922 | C2 | semidirect |
| 3. C2×#13133188 | C2 | semidirect |
| 4. #16810755 | C2 | direct (N × H) |
| 5. C2×#13133139 | C2 | semidirect |
| 6. C2×#13133138 | C2 | semidirect |
| 7. C2×#13133129 | C2 | semidirect |
| 8. C22×D8×C53 | C2 | semidirect |
| 16. C2×D4×D53 | C22 | semidirect |
| 19. C2×#11719922 | C22 | semidirect |
| 20. C22×#88322 | C22 | semidirect |
| 22. #13133188 | C22 | semidirect |
| 23. C2×C4⋊Dic53 | C22 | semidirect |
| 25. #13133139 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 27. #13133129 | C22 | semidirect |
| 29. C22×D4×C53 | C22 | semidirect |
| 31. C2×D8×C53 | C22 | semidirect |
| 32. C22×C8×C53 | C22 | semidirect |
| 46. C2×D4×C53 | D4 | semidirect |
| 48. C2×D4×C53 | C23 | semidirect |
| 61. C2×D212 | D4 | semidirect |
| 69. C2×C8×C53 | C23 | semidirect |
| 73. C4⋊Dic53 | C23 | semidirect |
| 75. C2×#88322 | C23 | semidirect |
| 95. C22×D53 | D8 | semidirect |
| 102. D4×C53 | C2×D4 | semidirect |
| 115. D212 | C2×D4 | semidirect |
| 141. C2×D53 | C2×D8 | semidirect |
| 150. C2×C53 | #447 | semidirect |
| 158. C22×D8 | D53 | semidirect |
| 164. C53 | C2×#447 | semidirect |
| 174. C22×D4 | C2×D53 | semidirect |
| 179. C2×D8 | C2×D53 | semidirect |
| 181. C22×C8 | C2×D53 | semidirect |
| 213. C2×D4 | C22⋊D53 | semidirect |
| 215. C2×D4 | C22×D53 | semidirect |
| 228. C2×C8 | C22×D53 | semidirect |
| 263. D4 | C2×C22⋊D53 | semidirect |
| 307. C2 | #16810755 | direct (N × H) |