Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20276992 | C2 | semidirect |
| 3. #20272896 | C2 | semidirect |
| 6. C32×Dic53 | C2 | semidirect |
| 7. C53×#1416 | C2 | semidirect |
| 85. #1416 | D53 | semidirect |
| 104. C53 | #13721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276992 | 2 |
| #20276977 | 2 |
| #20272896 | 2 |
| #20272894 | 2 |
| #20272892 | 2 |
| C32×Dic53 | 2 |
| C53×#1416 | 2 |
| #13721 | 53 |