Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 50 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. #20291119 | C2 | semidirect |
| 2. #20291113 | C2 | semidirect |
| 3. #20289880 | C2 | semidirect |
| 4. #20289870 | C2 | semidirect |
| 5. #20289868 | C2 | semidirect |
| 6. #20289824 | C2 | semidirect |
| 18. #16810462 | C4 | semidirect |
| 19. #16810461 | C4 | semidirect |
| 20. #16810458 | C4 | semidirect |
| 22. C53×D32 | C4 | semidirect |
| 34. Dic424 | C2×C4 | semidirect |
| 39. #13133123 | C2×C4 | semidirect |
| 41. D16×C53 | C2×C4 | semidirect |
| 42. C32×C53 | C2×C4 | semidirect |
| 110. D32 | #6157 | semidirect |
| 118. C53 | #13658 | semidirect |
| 128. D16 | C2×#6157 | semidirect |
| 138. C32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291119 | 2 |
| #20291113 | 2 |
| #20289880 | 2 |
| #20289870 | 2 |
| #20289868 | 2 |
| #20289824 | 2 |
| #20277026 | 2 |
| #13658 | 53 |