Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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×#16810456 | C2 | semidirect |
| 2. #20276798 | C2 | semidirect |
| 3. #20272917 | C2 | semidirect |
| 4. #20272893 | C2 | semidirect |
| 5. C2×C53×D32 | C2 | semidirect |
| 27. C32×C53 | D4 | semidirect |
| 66. C2×D32 | D53 | semidirect |
| 84. C53 | #13697 | semidirect |
| 97. C32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810456 | 2 |
| #20276798 | 2 |
| #20272917 | 2 |
| #20272893 | 2 |
| C2×C53×D32 | 2 |
| #13697 | 53 |