Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 171 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×Dic424 | C2 | semidirect |
| 2. C2×#16810461 | C2 | direct (N × H) |
| 3. C22×#13133123 | C2 | semidirect |
| 7. C2×Dic424 | C22 | semidirect |
| 8. #16810461 | C22 | direct (N × H) |
| 9. C2×#13133123 | C22 | semidirect |
| 18. Dic424 | C23 | semidirect |
| 19. #13133123 | C23 | semidirect |
| 58. C22×C53 | SD64 | semidirect |
| 68. C2×C53 | C2×SD64 | semidirect |
| 79. C53 | C22×SD64 | semidirect |
| 123. C22 | #16810461 | direct (N × H) |
| 129. C2 | C2×#16810461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic424 | 2 |
| C2×#16810461 | 2 |
| C22×#13133123 | 2 |
| C22×D16×C53 | 2 |
| C22×SD64 | 53 |