Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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. #20289427 | C2 | semidirect |
| 2. #20283419 | C2 | semidirect |
| 3. #20275134 | C2 | semidirect |
| 4. #20275003 | C2 | semidirect |
| 5. #20274666 | C2 | semidirect |
| 6. #20274517 | C2 | semidirect |
| 12. C22×#11719917 | C22 | semidirect |
| 15. #16810650 | C22 | semidirect |
| 18. #16810587 | C22 | semidirect |
| 19. #16810579 | C22 | semidirect |
| 20. #16810393 | C22 | semidirect |
| 35. C2×#11719917 | D4 | semidirect |
| 39. C22×#88322 | D4 | semidirect |
| 170. C53 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289427 | 2 |
| #20283419 | 2 |
| #20275134 | 2 |
| #20275003 | 2 |
| #20274666 | 2 |
| #20274517 | 2 |
| C53×#3025 | 2 |
| #21484 | 53 |