Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 19. #16810451 | C4 | semidirect |
| 20. #16810450 | C4 | semidirect |
| 21. #16810450 | C4 | semidirect |
| 22. C53×#367 | C4 | semidirect |
| 164. #367 | #6157 | semidirect |
| 167. C53 | #13111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290819 | 2 |
| #107×#6157 | 2 |
| #20289773 | 2 |
| #20289772 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #367×D53 | 2 |
| #13111 | 53 |