Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16810445 | C2 | semidirect |
| 5. #20275469 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 19. #16810423 | C4 | semidirect |
| 40. C2×#11719908 | C2×C4 | semidirect |
| 53. #107×C53 | C2×C4 | semidirect |
| 145. #1386 | D53 | semidirect |
| 168. C53 | #12956 | semidirect |
| 194. #107 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810734 | 2 |
| C2×#16810445 | 2 |
| C2×#16810437 | 2 |
| #20276430 | 2 |
| #20275469 | 2 |
| #20272794 | 2 |
| C53×#1386 | 2 |
| #12956 | 53 |