Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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 |
|---|---|---|
| 1. #20282906 | C2 | direct (N × H) |
| 2. C2×#16810565 | C2 | semidirect |
| 4. C2×#16810542 | C2 | semidirect |
| 11. #16810565 | C22 | semidirect |
| 13. #16810542 | C22 | semidirect |
| 114. C2×C53 | #2835 | semidirect |
| 133. C53 | C2×#2835 | semidirect |
| 219. C2 | #20282906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282906 | 2 |
| C2×#16810565 | 2 |
| C2×#16810548 | 2 |
| C2×#16810542 | 2 |
| C2×#16810495 | 2 |
| C2×C53×#393 | 2 |
| C2×#2835 | 53 |