Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20285091 | C2 | semidirect |
| 3. #20274013 | C2 | semidirect |
| 4. #20273310 | C2 | semidirect |
| 5. #20273307 | C2 | semidirect |
| 6. C53×#3550 | C2 | semidirect |
| 18. #16810365 | C22 | semidirect |
| 19. #16810363 | C22 | semidirect |
| 20. C53×#563 | C22 | semidirect |
| 161. #3550 | D53 | semidirect |
| 173. #563 | C2×D53 | semidirect |
| 194. C53 | #19077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285168 | 2 |
| #20285091 | 2 |
| #20274013 | 2 |
| #20273310 | 2 |
| #20273307 | 2 |
| C53×#3550 | 2 |
| #19077 | 53 |