Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 3. #20289626 | C2 | semidirect |
| 4. C16×#88324 | C2 | semidirect |
| 18. C2×#11719910 | C8 | semidirect |
| 26. #13133157 | C8 | semidirect |
| 33. M32×C53 | C8 | semidirect |
| 95. C53 | #11399 | semidirect |
| 100. M32 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811509 | 2 |
| #20289918 | 2 |
| #20289626 | 2 |
| C16×#88324 | 2 |
| M32×Dic53 | 2 |
| #11399 | 53 |