Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#16810462 | C2 | semidirect |
| 2. C2×#16810461 | C2 | semidirect |
| 3. C2×#16810458 | C2 | semidirect |
| 4. #20276973 | C2 | semidirect |
| 5. #20276963 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 7. C2×C53×D32 | C2 | semidirect |
| 37. #13133123 | D4 | semidirect |
| 45. C32×C53 | D4 | semidirect |
| 101. C2×D32 | D53 | semidirect |
| 125. C53 | #13729 | semidirect |
| 148. C32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| C2×#16810461 | 2 |
| C2×#16810458 | 2 |
| #20276973 | 2 |
| #20276963 | 2 |
| #20272848 | 2 |
| C2×C53×D32 | 2 |
| #13729 | 53 |