Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
668 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. #20275277 | C2 | semidirect |
| 4. #20274575 | C2 | semidirect |
| 6. C4×#13133128 | C2 | semidirect |
| 7. C53×#1745 | C2 | semidirect |
| 107. #1745 | D53 | semidirect |
| 128. C53 | #21433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277212 | 2 |
| #20275326 | 2 |
| #20275277 | 2 |
| #20274575 | 2 |
| #20274484 | 2 |
| C4×#13133128 | 2 |
| C53×#1745 | 2 |
| #21433 | 53 |