Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
780 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16811013 | C2 | semidirect |
| 2. C2×#16811012 | C2 | semidirect |
| 3. #20282760 | C2 | semidirect |
| 4. #20275539 | C2 | semidirect |
| 5. C2×#16810362 | C2 | semidirect |
| 6. #20272597 | C2 | semidirect |
| 7. C2×C53×#329 | C2 | semidirect |
| 49. #13133214 | D4 | semidirect |
| 61. #13133128 | D4 | semidirect |
| 79. #97×C53 | D4 | semidirect |
| 230. C2×#329 | D53 | semidirect |
| 263. C53 | #10078 | semidirect |
| 309. #97 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| C2×#16811012 | 2 |
| #20282760 | 2 |
| #20275539 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| C2×C53×#329 | 2 |
| #10078 | 53 |