Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #20272888 | C2 | semidirect |
| 5. #20272883 | C2 | semidirect |
| 6. #20272883 | C2 | semidirect |
| 7. C53×#1413 | C2 | semidirect |
| 152. #1413 | D53 | semidirect |
| 178. C53 | #13612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285799 | 2 |
| #20276408 | 2 |
| #20276403 | 2 |
| #20272888 | 2 |
| #20272883 | 2 |
| C53×#1413 | 2 |
| #13612 | 53 |