Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 434 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. #20280212 | C2 | semidirect |
| 3. #20273718 | C2 | semidirect |
| 4. #20272742 | C2 | semidirect |
| 5. #20272722 | C2 | semidirect |
| 6. #20272646 | C2 | semidirect |
| 7. C53×#1616 | C2 | semidirect |
| 190. #1616 | D53 | semidirect |
| 221. C53 | #12196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280212 | 2 |
| #20275757 | 2 |
| #20273718 | 2 |
| #20272742 | 2 |
| #20272722 | 2 |
| #20272646 | 2 |
| C53×#1616 | 2 |
| #12196 | 53 |