Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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. D53⋊(C4⋊C8) | C2 | semidirect |
| 3. #16811569 | C2 | semidirect |
| 4. #16811496 | C2 | semidirect |
| 15. C4×D212 | C4 | semidirect |
| 16. D4×Dic53 | C4 | semidirect |
| 17. #13133179 | C4 | semidirect |
| 23. C4×D4×C53 | C4 | semidirect |
| 74. D4×C53 | C4⋊C4 | semidirect |
| 88. D212 | C4⋊C4 | semidirect |
| 122. C4×C53 | #102 | semidirect |
| 127. Dic53 | #102 | semidirect |
| 145. C53 | #1802 | semidirect |
| 154. C4×D4 | #6157 | semidirect |
| 215. D4 | C4⋊#6157 | semidirect |
| 267. C4 | #13133279 | semidirect |