Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #20273387 | C2 | semidirect |
| 5. #20273110 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#2546 | C2 | semidirect |
| 208. #2546 | D53 | semidirect |
| 242. C53 | #10243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285836 | 2 |
| #20284187 | 2 |
| #20273387 | 2 |
| #20273209 | 2 |
| #20273110 | 2 |
| #20272618 | 2 |
| C53×#2546 | 2 |
| #10243 | 53 |