Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20283744 | C2 | semidirect |
| 2. C4×#13133134 | C2 | semidirect |
| 3. #20273313 | C2 | semidirect |
| 4. #20272579 | C2 | semidirect |
| 34. #13133128 | D4 | semidirect |
| 225. C53 | #9187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283744 | 2 |
| C4×#13133134 | 2 |
| #20273313 | 2 |
| #20272579 | 2 |
| C53×#2631 | 2 |
| #9187 | 53 |