Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20275756 | C2 | semidirect |
| 2. #20273751 | C2 | semidirect |
| 3. #20273649 | C2 | semidirect |
| 4. #20272742 | C2 | semidirect |
| 5. #20272718 | C2 | semidirect |
| 6. #20272647 | C2 | semidirect |
| 7. C53×#2828 | C2 | semidirect |
| 209. #2828 | D53 | semidirect |
| 243. C53 | #12198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275756 | 2 |
| #20273751 | 2 |
| #20273649 | 2 |
| #20272742 | 2 |
| #20272718 | 2 |
| #20272647 | 2 |
| C53×#2828 | 2 |
| #12198 | 53 |