Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16810420 | C2 | semidirect |
| 2. C2×#16810418 | C2 | semidirect |
| 3. #20272872 | C2 | direct (N × H) |
| 8. #16810420 | C22 | semidirect |
| 10. #16810418 | C22 | semidirect |
| 13. C2×#127×C53 | C4 | semidirect |
| 17. C53×#496 | C4 | semidirect |
| 19. C2×#97×C53 | C4 | semidirect |
| 41. #127×C53 | C2×C4 | semidirect |
| 50. #97×C53 | C2×C4 | semidirect |
| 163. C2×C53 | #1406 | semidirect |
| 167. C2×#127 | Dic53 | semidirect |
| 171. #496 | Dic53 | semidirect |
| 175. C2×#97 | Dic53 | semidirect |
| 180. C53 | C2×#1406 | semidirect |
| 197. #127 | C2×Dic53 | semidirect |
| 211. #97 | C2×Dic53 | semidirect |
| 319. C2 | #20272872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| C2×#16810418 | 2 |
| #20272872 | 2 |
| C2×C53×#496 | 2 |
| C2×#1406 | 53 |