Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1526 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1526 conjugacy classes of subgroups — too many to draw. Only its 360 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. #20290609 | C2 | direct (N × H) |
| 3. C2×#16811489 | C2 | semidirect |
| 8. #16811489 | C22 | semidirect |
| 126. C2×C53 | #1818 | semidirect |
| 144. C53 | C2×#1818 | semidirect |
| 250. C2 | #20290609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133274 | 2 |
| #20290609 | 2 |
| C2×#16811489 | 2 |
| C22×#13133175 | 2 |
| C2×#1818 | 53 |