Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 131 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. C22×#13133123 | C2 | semidirect |
| 2. C2×#16810449 | C2 | semidirect |
| 3. #20272893 | C2 | direct (N × H) |
| 7. C2×#13133123 | C22 | semidirect |
| 9. #16810449 | C22 | semidirect |
| 13. C2×D16×C53 | C4 | semidirect |
| 28. D16×C53 | C2×C4 | semidirect |
| 87. C2×C53 | #1415 | semidirect |
| 94. C2×D16 | Dic53 | semidirect |
| 102. C53 | C2×#1415 | semidirect |
| 112. D16 | C2×Dic53 | semidirect |
| 169. C2 | #20272893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133123 | 2 |
| C2×#16810449 | 2 |
| #20272893 | 2 |
| C22×D16×C53 | 2 |
| C2×#1415 | 53 |