Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 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. #20285293 | C2 | semidirect |
| 2. #20285292 | C2 | semidirect |
| 3. #20285142 | C2 | semidirect |
| 4. #20285138 | C2 | semidirect |
| 5. #20274388 | C2 | semidirect |
| 6. #20274386 | C2 | semidirect |
| 7. #20274384 | C2 | semidirect |
| 8. #20274382 | C2 | semidirect |
| 9. #20274380 | C2 | semidirect |
| 10. #322×D53 | C2 | semidirect |
| 11. C53×#1721 | C2 | semidirect |
| 135. C8×D53 | D8 | semidirect |
| 196. #1721 | D53 | semidirect |
| 235. C53 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285293 | 2 |
| #20285292 | 2 |
| #20285142 | 2 |
| #20285138 | 2 |
| #20274388 | 2 |
| #20274386 | 2 |
| #20274384 | 2 |
| #20274382 | 2 |
| #20274380 | 2 |
| #322×D53 | 2 |
| C53×#1721 | 2 |
| #19616 | 53 |