Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16810458 | C2 | semidirect |
| 2. C22×#13133123 | C2 | semidirect |
| 3. #20276801 | C2 | semidirect |
| 4. #20272914 | C2 | semidirect |
| 5. #20272893 | C2 | semidirect |
| 6. #20272892 | C2 | semidirect |
| 7. C53×#2215 | C2 | semidirect |
| 28. #13133123 | D4 | semidirect |
| 84. C22×C53 | D32 | semidirect |
| 97. #2215 | D53 | semidirect |
| 120. C53 | #13694 | semidirect |
| 186. C22 | #16810458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810458 | 2 |
| C22×#13133123 | 2 |
| #20276801 | 2 |
| #20272914 | 2 |
| #20272893 | 2 |
| #20272892 | 2 |
| C53×#2215 | 2 |
| #13694 | 53 |