Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
812 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20273992 | C2 | semidirect |
| 4. #20273957 | C2 | semidirect |
| 179. C53 | #18703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286106 | 2 |
| #20285225 | 2 |
| #20273992 | 2 |
| #20273957 | 2 |
| #20273453 | 2 |
| #20273170 | 2 |
| C53×#3556 | 2 |
| #18703 | 53 |