Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 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. #20276473 | C2 | semidirect |
| 3. C2×#16810438 | C2 | semidirect |
| 5. #20275628 | C2 | semidirect |
| 7. C53×#1381 | C2 | semidirect |
| 155. #1381 | D53 | semidirect |
| 178. C53 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| #20276473 | 2 |
| C2×#16810438 | 2 |
| C2×#16810435 | 2 |
| #20275628 | 2 |
| #20275623 | 2 |
| C53×#1381 | 2 |
| #13440 | 53 |