Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276552 | C2 | semidirect |
| 3. #20276551 | C2 | semidirect |
| 4. #20272790 | C2 | semidirect |
| 5. #20272689 | C2 | semidirect |
| 6. C8×#11719908 | C2 | semidirect |
| 7. C53×#1335 | C2 | semidirect |
| 25. #13133163 | C8 | semidirect |
| 26. #13133161 | C8 | semidirect |
| 27. #13133160 | C8 | semidirect |
| 28. #13133158 | C8 | semidirect |
| 104. #1335 | D53 | semidirect |
| 125. C53 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276594 | 2 |
| #20276552 | 2 |
| #20276551 | 2 |
| #20272790 | 2 |
| #20272689 | 2 |
| C8×#11719908 | 2 |
| C53×#1335 | 2 |
| #12046 | 53 |