Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1050 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 184 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. #20291207 | C2 | semidirect |
| 2. #20290847 | C2 | semidirect |
| 3. #20290710 | C2 | semidirect |
| 4. #20290637 | C2 | semidirect |
| 5. #20290433 | C2 | semidirect |
| 18. #16811000 | C4 | semidirect |
| 19. #16810999 | C4 | semidirect |
| 20. #16810998 | C4 | semidirect |
| 22. C53×#493 | C4 | semidirect |
| 36. C2×D424 | C2×C4 | semidirect |
| 37. C2×#11719922 | C2×C4 | semidirect |
| 40. #13133214 | C2×C4 | semidirect |
| 42. #13133213 | C2×C4 | semidirect |
| 44. C4×#88322 | C2×C4 | semidirect |
| 45. C8×Dic53 | C2×C4 | semidirect |
| 46. C2×D8×C53 | C2×C4 | semidirect |
| 47. #127×C53 | C2×C4 | semidirect |
| 48. C4×C8×C53 | C2×C4 | semidirect |
| 141. #493 | #6157 | semidirect |
| 151. C53 | #22276 | semidirect |
| 158. C2×D8 | C2×#6157 | semidirect |
| 164. #127 | C2×#6157 | semidirect |
| 175. C4×C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291207 | 2 |
| #20290847 | 2 |
| #20290710 | 2 |
| #20290637 | 2 |
| #20290433 | 2 |
| #493×D53 | 2 |
| #22276 | 53 |