Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #20277895 | C2 | semidirect |
| 3. #20273431 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1288 | C2 | semidirect |
| 11. #16810974 | C4 | semidirect |
| 12. #16810970 | C4 | semidirect |
| 152. #1288 | D53 | semidirect |
| 175. C53 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285109 | 2 |
| #20277895 | 2 |
| #20273431 | 2 |
| #20273263 | 2 |
| #20273261 | 2 |
| #20272580 | 2 |
| C53×#1288 | 2 |
| #9430 | 53 |