Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22⋊C16×D53 | C2 | semidirect |
| 3. #20272654 | C2 | semidirect |
| 4. #20272639 | C2 | semidirect |
| 5. C53×#1314 | C2 | semidirect |
| 56. C2×C22⋊D53 | C16 | semidirect |
| 88. C23×C53 | C2×C16 | semidirect |
| 111. C2×Dic53 | C2×C16 | semidirect |
| 147. #1314 | D53 | semidirect |
| 168. C53 | #11465 | semidirect |
| 243. C23 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810686 | 2 |
| C22⋊C16×D53 | 2 |
| #20272654 | 2 |
| #20272639 | 2 |
| C53×#1314 | 2 |
| #11465 | 53 |