Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20287116 | C2 | semidirect |
| 2. #20276909 | C2 | semidirect |
| 3. #20276897 | C2 | semidirect |
| 4. #20276869 | C2 | semidirect |
| 5. #20276819 | C2 | semidirect |
| 6. C4×D848 | C2 | semidirect |
| 7. #20276548 | C2 | semidirect |
| 8. #20276502 | C2 | semidirect |
| 9. C53×#2253 | C2 | semidirect |
| 135. #2253 | D53 | semidirect |
| 173. C53 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287116 | 2 |
| #20276909 | 2 |
| #20276897 | 2 |
| #20276869 | 2 |
| #20276819 | 2 |
| C4×D848 | 2 |
| #20276548 | 2 |
| #20276502 | 2 |
| C53×#2253 | 2 |
| #33922 | 53 |