Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20276632 | C2 | semidirect |
| 3. #20275722 | C2 | semidirect |
| 4. #20272727 | C2 | semidirect |
| 5. #20272725 | C2 | semidirect |
| 6. #20272638 | C2 | semidirect |
| 7. C53×#2188 | C2 | semidirect |
| 182. #2188 | D53 | semidirect |
| 214. C53 | #12107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285509 | 2 |
| #20276632 | 2 |
| #20275722 | 2 |
| #20272727 | 2 |
| #20272725 | 2 |
| #20272638 | 2 |
| C53×#2188 | 2 |
| #12107 | 53 |