Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20272777 | C2 | semidirect |
| 5. #20272776 | C2 | semidirect |
| 6. #20272775 | C2 | semidirect |
| 7. C53×#1366 | C2 | semidirect |
| 121. #1366 | D53 | semidirect |
| 143. C53 | #11956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285228 | 2 |
| #364×D53 | 2 |
| #20272777 | 2 |
| #20272776 | 2 |
| #20272775 | 2 |
| C53×#1366 | 2 |
| #11956 | 53 |