Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 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. #20276989 | C2 | semidirect |
| 3. #20272897 | C2 | semidirect |
| 4. #20272895 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 105. C53 | #13722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276989 | 2 |
| #20276973 | 2 |
| #20272897 | 2 |
| #20272895 | 2 |
| #20272893 | 2 |
| #20272848 | 2 |
| C53×#1415 | 2 |
| #13722 | 53 |