Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 79 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. #349×D53 | C2 | semidirect |
| 3. #338×D53 | C2 | semidirect |
| 4. #20272709 | C2 | semidirect |
| 5. #20272707 | C2 | semidirect |
| 6. #20272705 | C2 | semidirect |
| 7. C53×#1342 | C2 | semidirect |
| 199. #1342 | D53 | semidirect |
| 228. C53 | #11688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284326 | 2 |
| #349×D53 | 2 |
| #338×D53 | 2 |
| #20272709 | 2 |
| #20272707 | 2 |
| #20272705 | 2 |
| C53×#1342 | 2 |
| #11688 | 53 |