Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20272785 | C2 | semidirect |
| 2. C8×#11719908 | C2 | semidirect |
| 26. D8×C53 | C16 | semidirect |
| 82. C53 | #7068 | semidirect |
| 98. D8 | #11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272785 | 2 |
| C8×#11719908 | 2 |
| C8×D8×C53 | 2 |
| #7068 | 53 |