Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276326 | C2 | semidirect |
| 3. #20272640 | C2 | semidirect |
| 4. C2×C53×C22⋊C16 | C2 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 19. C53×C22⋊C16 | C22 | semidirect |
| 159. C2×C22⋊C16 | D53 | semidirect |
| 182. C22⋊C16 | C2×D53 | semidirect |
| 183. C53 | #11422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810589 | 2 |
| #20276326 | 2 |
| #20272640 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #11422 | 53 |