Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275695 | C2 | semidirect |
| 3. #20273435 | C2 | semidirect |
| 4. #20273352 | C2 | semidirect |
| 5. #20273224 | C2 | semidirect |
| 6. #20273223 | C2 | semidirect |
| 7. C53×#1557 | C2 | semidirect |
| 13. #16811278 | C4 | semidirect |
| 14. #16811277 | C4 | semidirect |
| 215. #1557 | D53 | semidirect |
| 250. C53 | #8494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289113 | 2 |
| #20275695 | 2 |
| #20273435 | 2 |
| #20273352 | 2 |
| #20273224 | 2 |
| #20273223 | 2 |
| C53×#1557 | 2 |
| #8494 | 53 |