Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20291571 | C2 | semidirect |
| 2. #20290176 | C2 | semidirect |
| 3. #20290054 | C2 | semidirect |
| 4. #20289986 | C2 | semidirect |
| 5. #20289580 | C2 | semidirect |
| 6. #20289560 | C2 | semidirect |
| 259. C53 | #9243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291571 | 2 |
| #20290176 | 2 |
| #20290054 | 2 |
| #20289986 | 2 |
| #20289580 | 2 |
| #20289560 | 2 |
| C2×#16810840 | 2 |
| #9243 | 53 |