Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20278006 | C2 | semidirect |
| 4. #20273145 | C2 | semidirect |
| 5. #20273144 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 131. C4×Dic53 | SD16 | semidirect |
| 237. C53 | #10014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284742 | 2 |
| #20278006 | 2 |
| #20275548 | 2 |
| #20273145 | 2 |
| #20273144 | 2 |
| #20272543 | 2 |
| C53×#3103 | 2 |
| #10014 | 53 |