Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16811063 | C2 | semidirect |
| 2. C22×#13133162 | C2 | semidirect |
| 4. #20283582 | C2 | semidirect |
| 5. #20276780 | C2 | semidirect |
| 6. #20276754 | C2 | semidirect |
| 7. #20276473 | C2 | semidirect |
| 8. #20276430 | C2 | semidirect |
| 9. C53×#2138 | C2 | semidirect |
| 16. C2×#13133163 | C22 | semidirect |
| 19. C2×#13133161 | C22 | semidirect |
| 25. #16810717 | C22 | semidirect |
| 28. #16810441 | C22 | semidirect |
| 33. C53×#358 | C22 | semidirect |
| 34. C53×#357 | C22 | semidirect |
| 40. C2×Dic212 | D4 | semidirect |
| 180. #2138 | D53 | semidirect |
| 208. #358 | C2×D53 | semidirect |
| 210. #357 | C2×D53 | semidirect |
| 211. C53 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| C22×#13133162 | 2 |
| #20285202 | 2 |
| #20283582 | 2 |
| #20276780 | 2 |
| #20276754 | 2 |
| #20276473 | 2 |
| #20276430 | 2 |
| C53×#2138 | 2 |
| #33587 | 53 |