Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
972 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 1. C2×#16810672 | C2 | semidirect |
| 3. #20276232 | C2 | semidirect |
| 4. C2×C53×#338 | C2 | semidirect |
| 111. C2×#338 | D53 | semidirect |
| 127. C53 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810672 | 2 |
| #20283159 | 2 |
| #20276232 | 2 |
| C2×C53×#338 | 2 |
| #23723 | 53 |