Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 3. #20272796 | C2 | semidirect |
| 4. #20272795 | C2 | semidirect |
| 5. C53×#1375 | C2 | semidirect |
| 129. #1375 | D53 | semidirect |
| 146. C53 | #12849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810575 | 2 |
| C2×#16810404 | 2 |
| #20272796 | 2 |
| #20272795 | 2 |
| C53×#1375 | 2 |
| #12849 | 53 |