Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1810 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 319 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. #20272977 | C2 | semidirect |
| 2. #20272964 | C2 | semidirect |
| 3. #20272956 | C2 | semidirect |
| 4. #20272952 | C2 | semidirect |
| 15. C53×#392 | C4 | semidirect |
| 166. #392 | Dic53 | semidirect |
| 171. C53 | #14651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272977 | 2 |
| #20272964 | 2 |
| #20272956 | 2 |
| #20272952 | 2 |
| C2×C53×#392 | 2 |
| #14651 | 53 |