Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
694 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20273432 | C2 | semidirect |
| 3. #20273341 | C2 | semidirect |
| 4. #20273341 | C2 | semidirect |
| 7. C53×#1556 | C2 | semidirect |
| 225. #1556 | D53 | semidirect |
| 263. C53 | #8525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811250 | 2 |
| #20273432 | 2 |
| #20273341 | 2 |
| #20273047 | 2 |
| C53×#1556 | 2 |
| #8525 | 53 |