Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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. #20273019 | C2 | semidirect |
| 3. #20273017 | C2 | semidirect |
| 4. #20273016 | C2 | semidirect |
| 5. #20273015 | C2 | semidirect |
| 6. #20273014 | C2 | semidirect |
| 7. C53×#1454 | C2 | semidirect |
| 18. #16810345 | C22 | semidirect |
| 19. #16810345 | C22 | semidirect |
| 20. #16810344 | C22 | semidirect |
| 21. C8×#88322 | C22 | semidirect |
| 23. C53×#322 | C22 | semidirect |
| 24. C82×C53 | C22 | semidirect |
| 101. #1454 | D53 | semidirect |
| 120. #322 | C2×D53 | semidirect |
| 122. C82 | C2×D53 | semidirect |
| 123. C53 | #17339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283343 | 2 |
| #20273019 | 2 |
| #20273017 | 2 |
| #20273016 | 2 |
| #20273015 | 2 |
| #20273014 | 2 |
| C53×#1454 | 2 |
| #17339 | 53 |