Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20274834 | C2 | semidirect |
| 4. #20273227 | C2 | semidirect |
| 6. #20272584 | C2 | semidirect |
| 7. C53×#1552 | C2 | semidirect |
| 154. #1552 | D53 | semidirect |
| 183. C53 | #10515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286027 | 2 |
| #20274834 | 2 |
| #20273408 | 2 |
| #20273227 | 2 |
| #20273224 | 2 |
| #20272584 | 2 |
| C53×#1552 | 2 |
| #10515 | 53 |