Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20273443 | C2 | semidirect |
| 4. #20273329 | C2 | semidirect |
| 6. #20272626 | C2 | semidirect |
| 7. C53×#1838 | C2 | semidirect |
| 150. #1838 | D53 | semidirect |
| 180. C53 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286103 | 2 |
| #20273443 | 2 |
| #20273435 | 2 |
| #20273329 | 2 |
| #20273325 | 2 |
| #20272626 | 2 |
| C53×#1838 | 2 |
| #10527 | 53 |