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×#13133243 | C2 | semidirect |
| 2. #16811190 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. #16810628 | C2 | semidirect |
| 5. C2×#13133134 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C2×#127×C53 | C2 | semidirect |
| 44. C2×D4×C53 | D4 | semidirect |
| 53. C2×D212 | D4 | semidirect |
| 55. C2×Dic106 | D4 | semidirect |
| 57. C42×C53 | D4 | semidirect |
| 62. C4⋊Dic53 | D4 | semidirect |
| 67. #11719917 | D4 | semidirect |
| 141. C2×#127 | D53 | semidirect |
| 146. C53 | #2002 | semidirect |
| 191. C2×D4 | C22⋊D53 | semidirect |
| 208. C42 | C22⋊D53 | semidirect |