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. #20284370 | C2 | semidirect |
| 4. C2×#16810440 | C2 | semidirect |
| 5. #20276432 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C2×C53×#350 | C2 | semidirect |
| 193. C2×#350 | 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×#16810893 | 2 |
| #20284370 | 2 |
| C2×#16810440 | 2 |
| #20276432 | 2 |
| #20272811 | 2 |
| C2×C53×#350 | 2 |
| #13320 | 53 |