Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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×#13133280 | C2 | semidirect |
| 13. C22×Dic106 | C4 | semidirect |
| 17. C2×Q8×D53 | C4 | semidirect |
| 21. C22×Q8×C53 | C4 | semidirect |
| 67. Q8×C53 | C22⋊C4 | semidirect |
| 88. Dic106 | C22⋊C4 | semidirect |
| 92. C22×C53 | #103 | semidirect |
| 98. C2×D53 | #103 | semidirect |
| 122. C53 | #1787 | semidirect |
| 130. C22×Q8 | #6157 | semidirect |
| 187. Q8 | C22⋊#6157 | semidirect |
| 219. C22 | #13133280 | semidirect |