Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810447 | C2 | semidirect |
| 3. C2×#16810446 | C2 | semidirect |
| 6. #20272823 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 19. #16810404 | C4 | semidirect |
| 153. #1387 | D53 | semidirect |
| 176. C53 | #12931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810670 | 2 |
| C2×#16810447 | 2 |
| C2×#16810446 | 2 |
| C2×#16810404 | 2 |
| #20274749 | 2 |
| #20272823 | 2 |
| C53×#1387 | 2 |
| #12931 | 53 |