Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20291671 | C2 | semidirect |
| 2. #20290853 | C2 | semidirect |
| 3. #20290087 | C2 | semidirect |
| 4. #20290075 | C2 | semidirect |
| 5. #20289604 | C2 | semidirect |
| 6. #20289600 | C2 | semidirect |
| 26. #16811032 | C4 | semidirect |
| 27. #16810987 | C4 | semidirect |
| 28. #16810982 | C4 | semidirect |
| 34. C53×#496 | C4 | semidirect |
| 226. #496 | #6157 | semidirect |
| 250. C53 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291671 | 2 |
| #20290853 | 2 |
| #20290087 | 2 |
| #20290075 | 2 |
| #20289604 | 2 |
| #20289600 | 2 |
| #20285307 | 2 |
| #8997 | 53 |