Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274464 | C2 | semidirect |
| 3. #20272539 | C2 | semidirect |
| 5. C53×#1839 | C2 | semidirect |
| 167. #1839 | D53 | semidirect |
| 196. C53 | #7608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277179 | 2 |
| #20274464 | 2 |
| #20272539 | 2 |
| #20272535 | 2 |
| C53×#1839 | 2 |
| #7608 | 53 |