Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 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×#16811059 | C2 | semidirect |
| 2. C2×#16810436 | C2 | semidirect |
| 3. #20275603 | C2 | semidirect |
| 4. #20272797 | C2 | semidirect |
| 5. C2×C53×#493 | C2 | semidirect |
| 24. C2×Dic212 | D4 | semidirect |
| 26. C2×D424 | D4 | semidirect |
| 31. #13133157 | D4 | semidirect |
| 143. C2×#493 | D53 | semidirect |
| 168. C53 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| C2×#16810436 | 2 |
| #20275603 | 2 |
| #20272797 | 2 |
| C2×C53×#493 | 2 |
| #13331 | 53 |