Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20291400 | C2 | semidirect |
| 2. #20290170 | C2 | semidirect |
| 3. #20290061 | C2 | semidirect |
| 4. #20290053 | C2 | semidirect |
| 5. #20289601 | C2 | semidirect |
| 6. #20289546 | C2 | semidirect |
| 241. C53 | #9213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291400 | 2 |
| #20290170 | 2 |
| #20290061 | 2 |
| #20290053 | 2 |
| #20289601 | 2 |
| #20289546 | 2 |
| #20284774 | 2 |
| #9213 | 53 |