Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#16811503 | C2 | semidirect |
| 2. #20289965 | C2 | semidirect |
| 3. #20289714 | C2 | semidirect |
| 4. #20289697 | C2 | semidirect |
| 218. C53 | #11766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811503 | 2 |
| #20289965 | 2 |
| #20289714 | 2 |
| #20289697 | 2 |
| #20280196 | 2 |
| #11766 | 53 |