Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1430 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1430 conjugacy classes of subgroups — too many to draw. Only its 280 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. #20290616 | C2 | direct (N × H) |
| 3. C2×#16811503 | C2 | semidirect |
| 9. #16811503 | C22 | semidirect |
| 146. C2×C53 | #1822 | semidirect |
| 164. C53 | C2×#1822 | semidirect |
| 288. C2 | #20290616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811595 | 2 |
| #20290616 | 2 |
| C2×#16811503 | 2 |
| C22×#13133174 | 2 |
| C2×#1822 | 53 |