Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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×#16811059 | C2 | semidirect |
| 2. #20284296 | C2 | semidirect |
| 3. #20276644 | C2 | semidirect |
| 4. #20276627 | C2 | semidirect |
| 5. #20276431 | C2 | semidirect |
| 6. #20276326 | C2 | semidirect |
| 7. C23×D8×C53 | C2 | semidirect |
| 8. C2×#13133239 | C22 | semidirect |
| 11. C2×#13133161 | C22 | semidirect |
| 12. C2×#13133158 | C22 | semidirect |
| 13. C2×#13133157 | C22 | semidirect |
| 14. #16810864 | C22 | semidirect |
| 15. #16810859 | C22 | semidirect |
| 17. #16810661 | C22 | semidirect |
| 19. #16810424 | C22 | semidirect |
| 20. C22⋊#11719908 | C22 | semidirect |
| 30. C2×Dic212 | C23 | semidirect |
| 32. C2×D424 | C23 | semidirect |
| 42. C2×#11719908 | C23 | semidirect |
| 43. #13133151 | C23 | semidirect |
| 61. C2×D8×C53 | D4 | semidirect |
| 163. C22×C53 | #509 | semidirect |
| 173. C23×D8 | D53 | semidirect |
| 206. C53 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D53 | semidirect |
| 343. C22 | #16811059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| #20284296 | 2 |
| #20276644 | 2 |
| #20276627 | 2 |
| #20276431 | 2 |
| #20276326 | 2 |
| C23×D8×C53 | 2 |
| #33517 | 53 |