Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 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 |
|---|---|---|
| 1. #20285277 | C2 | semidirect |
| 2. #20285276 | C2 | semidirect |
| 3. #20285224 | C2 | semidirect |
| 5. #20274346 | C2 | semidirect |
| 6. #20274344 | C2 | semidirect |
| 7. #20274343 | C2 | semidirect |
| 8. #20274340 | C2 | semidirect |
| 9. #20274339 | C2 | semidirect |
| 10. #322×D53 | C2 | semidirect |
| 11. C53×#1716 | C2 | semidirect |
| 130. C8×D53 | SD16 | semidirect |
| 181. #1716 | D53 | semidirect |
| 223. C53 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285277 | 2 |
| #20285276 | 2 |
| #20285224 | 2 |
| #20285144 | 2 |
| #20274346 | 2 |
| #20274344 | 2 |
| #20274343 | 2 |
| #20274340 | 2 |
| #20274339 | 2 |
| #322×D53 | 2 |
| C53×#1716 | 2 |
| #19608 | 53 |