Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291604 | C2 | semidirect |
| 2. #20290104 | C2 | semidirect |
| 3. #20290104 | C2 | semidirect |
| 4. #20290075 | C2 | semidirect |
| 5. #20289572 | C2 | semidirect |
| 6. #20289538 | C2 | semidirect |
| 22. #16810995 | C4 | semidirect |
| 23. #16810974 | C4 | semidirect |
| 24. #16810969 | C4 | semidirect |
| 28. C53×#493 | C4 | semidirect |
| 188. #493 | #6157 | semidirect |
| 207. C53 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291604 | 2 |
| #20290104 | 2 |
| #20290075 | 2 |
| #20289572 | 2 |
| #20289538 | 2 |
| #20285643 | 2 |
| #9281 | 53 |