Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 2. C22×C4⋊#6157 | C2 | semidirect |
| 4. #16811570 | C2 | direct (N × H) |
| 5. C2×(C2×#6157)⋊C4 | C2 | semidirect |
| 14. C2×C4⋊#6157 | C22 | semidirect |
| 17. (C2×#6157)⋊C4 | C22 | semidirect |
| 20. C2×C22⋊Dic53 | C4 | semidirect |
| 21. C2×#11719921 | C4 | semidirect |
| 22. C22⋊C4×D53 | C4 | semidirect |
| 24. C2×C22⋊C4×C53 | C4 | semidirect |
| 47. C22×C4×C53 | C2×C4 | semidirect |
| 48. C22×Dic53 | C2×C4 | semidirect |
| 51. C2×C4×D53 | C2×C4 | semidirect |
| 55. C22⋊C4×C53 | C2×C4 | semidirect |
| 56. C22⋊Dic53 | C2×C4 | semidirect |
| 57. #11719921 | C2×C4 | semidirect |
| 59. C23×C53 | C4⋊C4 | semidirect |
| 69. C22×D53 | C4⋊C4 | semidirect |
| 70. C22×D53 | C4⋊C4 | semidirect |
| 92. C2×C4×C53 | C22×C4 | semidirect |
| 94. C2×Dic53 | C22×C4 | semidirect |
| 101. C22×C53 | C2×C4⋊C4 | semidirect |
| 111. C2×D53 | C2×C4⋊C4 | semidirect |
| 127. C2×C53 | #385 | semidirect |
| 131. D53 | #385 | semidirect |
| 141. C53 | C2×#385 | semidirect |
| 158. C2×C22⋊C4 | #6157 | semidirect |
| 187. C22×C4 | C2×#6157 | semidirect |
| 192. C22⋊C4 | C2×#6157 | semidirect |
| 212. C23 | C4⋊#6157 | semidirect |
| 232. C2×C4 | C22×#6157 | semidirect |
| 252. C22 | C2×C4⋊#6157 | semidirect |
| 266. C2 | #16811570 | direct (N × H) |