Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20277461 | C2 | semidirect |
| 4. #20273401 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 10. #16811021 | C4 | semidirect |
| 11. #16810970 | C4 | semidirect |
| 181. #1286 | D53 | semidirect |
| 208. C53 | #9302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285845 | 2 |
| #20277461 | 2 |
| #20275546 | 2 |
| #20273401 | 2 |
| #20273274 | 2 |
| #20272543 | 2 |
| C53×#1286 | 2 |
| #9302 | 53 |