Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20274765 | C2 | semidirect |
| 3. #20272707 | C2 | semidirect |
| 4. C53×#2115 | C2 | semidirect |
| 15. #16810381 | C22 | semidirect |
| 19. C53×#349 | C22 | semidirect |
| 145. #2115 | D53 | semidirect |
| 167. #349 | C2×D53 | semidirect |
| 169. C53 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284363 | 2 |
| #20274765 | 2 |
| #20272707 | 2 |
| C53×#2115 | 2 |
| #11870 | 53 |