Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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×#16810453 | C2 | semidirect |
| 4. #20272808 | C2 | semidirect |
| 5. C2×C53×#368 | C2 | semidirect |
| 112. C2×#368 | D53 | semidirect |
| 132. C53 | #12838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133156 | 2 |
| C2×#16810453 | 2 |
| #20274750 | 2 |
| #20272808 | 2 |
| C2×C53×#368 | 2 |
| #12838 | 53 |