Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290262 | C2 | semidirect |
| 2. #20290016 | C2 | semidirect |
| 3. #20290014 | C2 | semidirect |
| 4. #20289956 | C2 | semidirect |
| 5. #20289955 | C2 | semidirect |
| 6. #20289928 | C2 | semidirect |
| 237. C53 | #9670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290262 | 2 |
| #20290016 | 2 |
| #20290014 | 2 |
| #20289956 | 2 |
| #20289955 | 2 |
| #20289928 | 2 |
| C2×#16810703 | 2 |
| #9670 | 53 |