Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20291560 | C2 | semidirect |
| 2. #20290478 | C2 | semidirect |
| 3. #20290171 | C2 | semidirect |
| 4. #20290106 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289581 | C2 | semidirect |
| 25. #16810905 | C4 | semidirect |
| 26. #16810824 | C4 | semidirect |
| 27. #16810818 | C4 | semidirect |
| 32. C53×#474 | C4 | semidirect |
| 214. #474 | #6157 | semidirect |
| 235. C53 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291560 | 2 |
| #20290478 | 2 |
| #20290171 | 2 |
| #20290106 | 2 |
| #20289602 | 2 |
| #20289581 | 2 |
| #20284868 | 2 |
| #9162 | 53 |