Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#13133245 | C2 | semidirect |
| 2. #16811192 | C2 | semidirect |
| 3. C2×#13133214 | C2 | semidirect |
| 4. C2×#13133145 | C2 | semidirect |
| 5. #16810627 | C2 | semidirect |
| 6. C2×#13133133 | C2 | semidirect |
| 7. C53×#339 | C2 | semidirect |
| 52. C2×D212 | D4 | semidirect |
| 53. C2×D212 | D4 | semidirect |
| 55. C2×Dic106 | D4 | semidirect |
| 57. M16×C53 | D4 | semidirect |
| 59. C4⋊C4×C53 | D4 | semidirect |
| 63. C42×C53 | D4 | semidirect |
| 145. #339 | D53 | semidirect |
| 146. C53 | #2002 | semidirect |
| 200. M16 | D212 | semidirect |
| 203. C4⋊C4 | D212 | semidirect |
| 208. C42 | D212 | semidirect |