Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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×D53⋊C8 | C2 | semidirect |
| 2. C22×C4⋊#6157 | C2 | semidirect |
| 3. C2×#13133279 | C2 | direct (N × H) |
| 7. C2×D53⋊C8 | C22 | semidirect |
| 10. C2×C4⋊#6157 | C22 | semidirect |
| 11. #13133279 | C22 | direct (N × H) |
| 13. C22×D212 | C4 | semidirect |
| 17. C2×D4×D53 | C4 | semidirect |
| 20. C22×D4×C53 | C4 | semidirect |
| 31. C2×D4×C53 | C2×C4 | semidirect |
| 39. D4×D53 | C2×C4 | semidirect |
| 42. C2×D212 | C2×C4 | semidirect |
| 49. C4⋊#6157 | C23 | semidirect |
| 51. D53⋊C8 | C23 | semidirect |
| 69. D4×C53 | C22×C4 | semidirect |
| 77. D212 | C22×C4 | semidirect |
| 86. C22×C53 | #102 | semidirect |
| 93. C2×D53 | #102 | semidirect |
| 105. C2×C53 | C2×#102 | semidirect |
| 108. D53 | C2×#102 | semidirect |
| 115. C53 | C22×#102 | semidirect |
| 123. C22×D4 | #6157 | semidirect |
| 149. C2×D4 | C2×#6157 | semidirect |
| 182. D4 | C22×#6157 | semidirect |
| 207. C22 | #13133279 | direct (N × H) |
| 219. C2 | C2×#13133279 | direct (N × H) |