Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1328 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 279 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 |
|---|---|---|
| 2. #20283407 | C2 | semidirect |
| 3. #20275133 | C2 | semidirect |
| 4. #20275001 | C2 | semidirect |
| 5. #20274666 | C2 | semidirect |
| 6. #20274515 | C2 | semidirect |
| 7. C53×#3573 | C2 | semidirect |
| 8. C22×C8×D53 | C22 | semidirect |
| 14. #16810651 | C22 | semidirect |
| 18. #16810586 | C22 | semidirect |
| 19. #16810578 | C22 | semidirect |
| 20. #16810394 | C22 | semidirect |
| 57. C2×M16×C53 | D4 | semidirect |
| 60. C22×C8×C53 | D4 | semidirect |
| 141. #3573 | D53 | semidirect |
| 170. C53 | #21483 | semidirect |
| 185. C2×M16 | C22⋊D53 | semidirect |
| 191. C22×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284107 | 2 |
| #20283407 | 2 |
| #20275133 | 2 |
| #20275001 | 2 |
| #20274666 | 2 |
| #20274515 | 2 |
| C53×#3573 | 2 |
| #21483 | 53 |