Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
186 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #20276597 | C2 | semidirect |
| 3. #20272918 | C2 | semidirect |
| 4. #20272899 | C2 | semidirect |
| 5. #20272898 | C2 | semidirect |
| 6. C4×#13133123 | C2 | semidirect |
| 7. C53×#2178 | C2 | semidirect |
| 10. #16810463 | C4 | semidirect |
| 11. #16810461 | C4 | semidirect |
| 12. #16810460 | C4 | semidirect |
| 13. #16810458 | C4 | semidirect |
| 90. #2178 | D53 | semidirect |
| 114. C53 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277022 | 2 |
| #20276597 | 2 |
| #20272918 | 2 |
| #20272899 | 2 |
| #20272898 | 2 |
| C4×#13133123 | 2 |
| C53×#2178 | 2 |
| #13655 | 53 |