Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20291107 | C2 | semidirect |
| 2. #20291105 | C2 | semidirect |
| 3. #20289743 | C2 | semidirect |
| 4. #20289680 | C2 | semidirect |
| 5. #20289679 | C2 | semidirect |
| 6. #20289631 | C2 | semidirect |
| 35. #13133163 | C8 | semidirect |
| 36. #13133161 | C8 | semidirect |
| 37. #13133160 | C8 | semidirect |
| 38. #13133158 | C8 | semidirect |
| 124. C53 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291107 | 2 |
| #20291105 | 2 |
| #20289743 | 2 |
| #20289680 | 2 |
| #20289679 | 2 |
| #20289631 | 2 |
| #20276598 | 2 |
| #12068 | 53 |