Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20272806 | C2 | semidirect |
| 4. #20272793 | C2 | semidirect |
| 5. C2×C53×#500 | C2 | semidirect |
| 21. C2×D424 | Q8 | semidirect |
| 133. C2×#500 | D53 | semidirect |
| 157. C53 | #13363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810423 | 2 |
| #20275581 | 2 |
| #20272806 | 2 |
| #20272793 | 2 |
| C2×C53×#500 | 2 |
| #13363 | 53 |