Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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×C4⋊#6157 | C2 | semidirect |
| 2. C2×#13133279 | C2 | semidirect |
| 3. D53⋊(C22⋊C8) | C2 | semidirect |
| 4. #16811496 | C2 | semidirect |
| 17. #13133192 | C4 | semidirect |
| 18. #13133191 | C4 | semidirect |
| 21. #13133188 | C4 | semidirect |
| 24. #121×C53 | C4 | semidirect |
| 32. C2×D4×C53 | C2×C4 | semidirect |
| 43. C2×D212 | C2×C4 | semidirect |
| 54. C4⋊#6157 | D4 | semidirect |
| 57. C4⋊C4×C53 | C2×C4 | semidirect |
| 62. C4⋊Dic53 | C2×C4 | semidirect |
| 114. C22×C53 | #102 | semidirect |
| 129. C2×D53 | #102 | semidirect |
| 160. C53 | #1874 | semidirect |
| 171. #121 | #6157 | semidirect |
| 192. C2×D4 | C2×#6157 | semidirect |
| 214. C4⋊C4 | C2×#6157 | semidirect |
| 289. C22 | #13133279 | semidirect |