Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16810439 | C2 | semidirect |
| 3. #20276435 | C2 | semidirect |
| 5. #20275463 | C2 | semidirect |
| 6. #20272797 | C2 | semidirect |
| 184. C53 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810439 | 2 |
| C2×#16810436 | 2 |
| #20276435 | 2 |
| #20276431 | 2 |
| #20275463 | 2 |
| #20272797 | 2 |
| C2×C53×#495 | 2 |
| #13414 | 53 |