Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16811013 | C2 | semidirect |
| 2. #20275538 | C2 | semidirect |
| 3. C2×#16810363 | C2 | semidirect |
| 4. #20272596 | C2 | semidirect |
| 5. C53×#2819 | C2 | semidirect |
| 30. #13133214 | D4 | semidirect |
| 34. #13133128 | D4 | semidirect |
| 141. #2819 | D53 | semidirect |
| 165. C53 | #10078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| #20275538 | 2 |
| C2×#16810363 | 2 |
| #20272596 | 2 |
| C53×#2819 | 2 |
| #10078 | 53 |