Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20272626 | C2 | semidirect |
| 4. #20272625 | C2 | semidirect |
| 5. C53×#1307 | C2 | semidirect |
| 125. #1307 | D53 | semidirect |
| 145. C53 | #8122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283347 | 2 |
| #20283345 | 2 |
| #20272626 | 2 |
| #20272625 | 2 |
| C53×#1307 | 2 |
| #8122 | 53 |