Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #20283782 | C2 | semidirect |
| 3. #20274681 | C2 | semidirect |
| 4. #20272843 | C2 | semidirect |
| 5. C53×#2126 | C2 | semidirect |
| 8. #16810805 | C4 | semidirect |
| 10. #16810795 | C4 | semidirect |
| 191. #2126 | D53 | semidirect |
| 219. C53 | #13054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284063 | 2 |
| #20283782 | 2 |
| #20274681 | 2 |
| #20272843 | 2 |
| C53×#2126 | 2 |
| #13054 | 53 |