Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
942 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20285710 | C2 | semidirect |
| 2. #20285063 | C2 | semidirect |
| 3. #20274038 | C2 | semidirect |
| 4. #20274008 | C2 | semidirect |
| 5. #20273353 | C2 | semidirect |
| 6. #20273326 | C2 | semidirect |
| 7. C53×#3548 | C2 | semidirect |
| 158. #3548 | D53 | semidirect |
| 192. C53 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285710 | 2 |
| #20285063 | 2 |
| #20274038 | 2 |
| #20274008 | 2 |
| #20273353 | 2 |
| #20273326 | 2 |
| C53×#3548 | 2 |
| #19061 | 53 |