Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16810422 | C2 | semidirect |
| 3. #20272883 | C2 | semidirect |
| 4. #20272881 | C2 | semidirect |
| 5. C2×C53×#356 | C2 | semidirect |
| 165. C2×#356 | D53 | semidirect |
| 190. C53 | #13590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285172 | 2 |
| C2×#16810422 | 2 |
| #20272883 | 2 |
| #20272881 | 2 |
| C2×C53×#356 | 2 |
| #13590 | 53 |