Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #20273059 | C2 | semidirect |
| 3. #20272741 | C2 | semidirect |
| 5. C53×#1801 | C2 | semidirect |
| 169. #1801 | D53 | semidirect |
| 196. C53 | #11829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277998 | 2 |
| #20273059 | 2 |
| #20272741 | 2 |
| #20272717 | 2 |
| C53×#1801 | 2 |
| #11829 | 53 |