Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291683 | C2 | semidirect |
| 2. C2×#16811540 | C2 | semidirect |
| 3. #20291031 | C2 | semidirect |
| 4. #20290603 | C2 | semidirect |
| 5. #20289792 | C2 | semidirect |
| 6. #20289781 | C2 | semidirect |
| 25. #16810895 | C4 | semidirect |
| 26. #16810894 | C4 | semidirect |
| 27. #16810893 | C4 | semidirect |
| 32. C53×#473 | C4 | semidirect |
| 238. #473 | #6157 | semidirect |
| 252. C53 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291683 | 2 |
| C2×#16811540 | 2 |
| #20291031 | 2 |
| #20290603 | 2 |
| #20289792 | 2 |
| #20289781 | 2 |
| #20284437 | 2 |
| #13070 | 53 |