Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20275488 | C2 | semidirect |
| 4. C2×#16810369 | C2 | semidirect |
| 6. #20272564 | C2 | semidirect |
| 7. C53×#1546 | C2 | semidirect |
| 182. #1546 | D53 | semidirect |
| 211. C53 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285172 | 2 |
| #20275488 | 2 |
| #20273393 | 2 |
| C2×#16810369 | 2 |
| #20273115 | 2 |
| #20272564 | 2 |
| C53×#1546 | 2 |
| #10550 | 53 |