Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20274868 | C2 | semidirect |
| 3. #20273498 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272566 | C2 | semidirect |
| 210. C53 | #8876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283854 | 2 |
| #20274868 | 2 |
| #20273498 | 2 |
| #20273201 | 2 |
| #20272609 | 2 |
| #20272566 | 2 |
| C53×#1483 | 2 |
| #8876 | 53 |