Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276840 | C2 | semidirect |
| 4. #20272919 | C2 | semidirect |
| 5. #20272909 | C2 | semidirect |
| 6. #20272906 | C2 | semidirect |
| 7. C53×#2258 | C2 | semidirect |
| 89. #2258 | D53 | semidirect |
| 114. C53 | #13702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| #20276840 | 2 |
| #20276835 | 2 |
| #20272919 | 2 |
| #20272909 | 2 |
| #20272906 | 2 |
| C53×#2258 | 2 |
| #13702 | 53 |