Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20275558 | C2 | semidirect |
| 4. #20273431 | C2 | semidirect |
| 6. #20272588 | C2 | semidirect |
| 7. C53×#1307 | C2 | semidirect |
| 187. #1307 | D53 | semidirect |
| 219. C53 | #9339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285947 | 2 |
| #20283882 | 2 |
| #20275558 | 2 |
| #20273431 | 2 |
| #20273323 | 2 |
| #20272588 | 2 |
| C53×#1307 | 2 |
| #9339 | 53 |