Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276944 | C2 | semidirect |
| 2. #20276765 | C2 | semidirect |
| 4. #20272773 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 90. D4×C53 | Q32 | semidirect |
| 152. C53 | #12346 | semidirect |
| 220. D4 | #13133163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276944 | 2 |
| #20276765 | 2 |
| #20274080 | 2 |
| #20272773 | 2 |
| #20272679 | 2 |
| D4⋊#11719908 | 2 |
| C53×#3338 | 2 |
| #12346 | 53 |