Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#13133162 | C2 | semidirect |
| 3. #20284371 | C2 | semidirect |
| 4. C2×#16810438 | C2 | semidirect |
| 5. #20276430 | C2 | semidirect |
| 6. C2×#16810406 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 194. #1382 | D53 | semidirect |
| 222. C53 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C2×#16810894 | 2 |
| #20284371 | 2 |
| C2×#16810438 | 2 |
| #20276430 | 2 |
| C2×#16810406 | 2 |
| C53×#1382 | 2 |
| #13320 | 53 |