Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. #20289823 | C2 | semidirect |
| 3. #20289820 | C2 | semidirect |
| 5. #16811555 | C4 | semidirect |
| 14. #13133267 | C2×C4 | semidirect |
| 65. Dic53 | M64 | semidirect |
| 82. C53 | C4×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811555 | 2 |
| #20289823 | 2 |
| #20289820 | 2 |
| C2×C16×Dic53 | 2 |
| C4×M64 | 53 |