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. #20273309 | C2 | semidirect |
| 4. #20273171 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#1278 | C2 | semidirect |
| 193. #1278 | 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 |
|---|---|
| #20284787 | 2 |
| #20283357 | 2 |
| #20273309 | 2 |
| #20273171 | 2 |
| #20273155 | 2 |
| #20272606 | 2 |
| C53×#1278 | 2 |
| #9214 | 53 |