Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20273163 | C2 | semidirect |
| 5. #20273058 | C2 | semidirect |
| 6. #20272627 | C2 | semidirect |
| 7. C53×#1291 | C2 | semidirect |
| 196. #1291 | D53 | semidirect |
| 229. C53 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284888 | 2 |
| #20283700 | 2 |
| #20273344 | 2 |
| #20273163 | 2 |
| #20273058 | 2 |
| #20272627 | 2 |
| C53×#1291 | 2 |
| #9531 | 53 |