Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16811063 | C2 | semidirect |
| 2. C2×#16810433 | C2 | semidirect |
| 3. #20275586 | C2 | semidirect |
| 4. #20272799 | C2 | semidirect |
| 26. C2×Dic212 | D4 | semidirect |
| 31. #13133157 | D4 | semidirect |
| 175. C53 | #13342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| C2×#16810433 | 2 |
| #20275586 | 2 |
| #20272799 | 2 |
| C53×#3150 | 2 |
| #13342 | 53 |