Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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×#16810764 | C2 | semidirect |
| 3. C2×#16810761 | C2 | semidirect |
| 4. #20274638 | C2 | semidirect |
| 5. #20273076 | C2 | semidirect |
| 6. #20272603 | C2 | semidirect |
| 7. C53×#1471 | C2 | semidirect |
| 222. #1471 | D53 | semidirect |
| 255. C53 | #9988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| C2×#16810764 | 2 |
| C2×#16810761 | 2 |
| #20274638 | 2 |
| #20273076 | 2 |
| #20272603 | 2 |
| C53×#1471 | 2 |
| #9988 | 53 |