Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #20274650 | C2 | semidirect |
| 4. #20272582 | C2 | semidirect |
| 17. C53×#395 | C4 | semidirect |
| 18. C53×#393 | C4 | semidirect |
| 199. #395 | Dic53 | semidirect |
| 200. #393 | Dic53 | semidirect |
| 207. C53 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283744 | 2 |
| #20274703 | 2 |
| #20274650 | 2 |
| #20272582 | 2 |
| C53×#2409 | 2 |
| #9471 | 53 |