Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16810419 | C2 | semidirect |
| 3. C4×#13133136 | C2 | semidirect |
| 4. C53×#1801 | C2 | semidirect |
| 36. #13133136 | D4 | semidirect |
| 156. C4×C53 | #355 | semidirect |
| 160. #1801 | D53 | semidirect |
| 184. C53 | #13226 | semidirect |
| 320. C4 | #16810419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279714 | 2 |
| C2×#16810419 | 2 |
| C4×#13133136 | 2 |
| C53×#1801 | 2 |
| #13226 | 53 |