Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20273170 | C2 | semidirect |
| 5. #20272605 | C2 | semidirect |
| 6. #20272553 | C2 | semidirect |
| 7. C53×#1526 | C2 | semidirect |
| 189. #1526 | D53 | semidirect |
| 222. C53 | #9214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284780 | 2 |
| #20283360 | 2 |
| #20273170 | 2 |
| #20273155 | 2 |
| #20272605 | 2 |
| #20272553 | 2 |
| C53×#1526 | 2 |
| #9214 | 53 |