Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20272916 | C2 | semidirect |
| 4. #20272910 | C2 | semidirect |
| 7. C53×#1423 | C2 | semidirect |
| 78. #1423 | D53 | semidirect |
| 97. C53 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276992 | 2 |
| #20276561 | 2 |
| #20272916 | 2 |
| #20272910 | 2 |
| #20272894 | 2 |
| #20272892 | 2 |
| C53×#1423 | 2 |
| #13707 | 53 |