Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16810457 | C2 | semidirect |
| 2. #20276499 | C2 | semidirect |
| 3. #20272893 | C2 | semidirect |
| 7. C2×#13133123 | C22 | semidirect |
| 9. #16810449 | C22 | semidirect |
| 13. C2×D16×C53 | C4 | semidirect |
| 89. C2×D16 | Dic53 | semidirect |
| 97. C53 | #13617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810457 | 2 |
| #20276499 | 2 |
| #20272893 | 2 |
| C22×D16×C53 | 2 |
| #13617 | 53 |