Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20273136 | C2 | semidirect |
| 5. #20273071 | C2 | semidirect |
| 6. #20272586 | C2 | semidirect |
| 7. C53×#3236 | C2 | semidirect |
| 174. #3236 | D53 | semidirect |
| 211. C53 | #10123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285913 | 2 |
| #20285118 | 2 |
| #20273183 | 2 |
| #20273136 | 2 |
| #20273071 | 2 |
| #20272586 | 2 |
| C53×#3236 | 2 |
| #10123 | 53 |