Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810450 | C2 | semidirect |
| 2. C2×#16810448 | C2 | semidirect |
| 6. #20272793 | C2 | semidirect |
| 7. C53×#1846 | C2 | semidirect |
| 144. #1846 | D53 | semidirect |
| 167. C53 | #13528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810450 | 2 |
| C2×#16810448 | 2 |
| C2×#16810423 | 2 |
| #20275581 | 2 |
| #20272793 | 2 |
| C53×#1846 | 2 |
| #13528 | 53 |