Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20276964 | C2 | semidirect |
| 2. #20276792 | C2 | semidirect |
| 3. #20276788 | C2 | semidirect |
| 4. #20276551 | C2 | semidirect |
| 5. #20272790 | C2 | semidirect |
| 6. #20272751 | C2 | semidirect |
| 7. C53×#1357 | C2 | semidirect |
| 112. #1357 | D53 | semidirect |
| 133. C53 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276964 | 2 |
| #20276792 | 2 |
| #20276788 | 2 |
| #20276551 | 2 |
| #20272790 | 2 |
| #20272751 | 2 |
| C53×#1357 | 2 |
| #12436 | 53 |