Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#16810672 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. #20272830 | C2 | semidirect |
| 5. C2×C53×#349 | C2 | semidirect |
| 40. #13133153 | D4 | semidirect |
| 152. C2×#349 | D53 | semidirect |
| 175. C53 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284324 | 2 |
| C2×#16810672 | 2 |
| #20276444 | 2 |
| #20272830 | 2 |
| C2×C53×#349 | 2 |
| #12998 | 53 |