Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20277030 | C2 | semidirect |
| 2. #20276965 | C2 | semidirect |
| 3. #20276597 | C2 | semidirect |
| 4. #20272906 | C2 | semidirect |
| 5. C53×#1422 | C2 | semidirect |
| 22. Dic424 | D4 | semidirect |
| 27. D848 | D4 | semidirect |
| 80. #1422 | D53 | semidirect |
| 97. C53 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277030 | 2 |
| #20276965 | 2 |
| #20276597 | 2 |
| #20272906 | 2 |
| C53×#1422 | 2 |
| #13692 | 53 |