Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. #20272639 | C2 | semidirect |
| 2. #20272583 | C2 | semidirect |
| 6. C22×D8×C53 | C4 | semidirect |
| 10. C53×#340 | C4 | semidirect |
| 136. C22×D8 | Dic53 | semidirect |
| 142. #340 | Dic53 | semidirect |
| 143. C53 | #7076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272639 | 2 |
| #20272583 | 2 |
| C53×#1999 | 2 |
| #7076 | 53 |