Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#16810445 | C2 | semidirect |
| 5. #20272813 | C2 | semidirect |
| 6. #20272797 | C2 | semidirect |
| 7. C53×#1941 | C2 | semidirect |
| 18. #16810432 | C4 | semidirect |
| 92. Dic212 | C4⋊C4 | semidirect |
| 94. D424 | C4⋊C4 | semidirect |
| 155. #1941 | D53 | semidirect |
| 180. C53 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810741 | 2 |
| C2×#16810445 | 2 |
| C2×#16810432 | 2 |
| #20272813 | 2 |
| #20272797 | 2 |
| C53×#1941 | 2 |
| #12950 | 53 |