Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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. D4×#11719940 | C2 | semidirect |
| 2. #20290857 | C2 | semidirect |
| 3. #20290222 | C2 | semidirect |
| 4. #20290040 | C2 | semidirect |
| 5. #20289585 | C2 | semidirect |
| 6. #20289560 | C2 | semidirect |
| 132. #11719940 | D8 | semidirect |
| 182. D4×C53 | #100 | semidirect |
| 300. C53 | #9253 | semidirect |
| 459. D4 | #13133277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719940 | 2 |
| #20290857 | 2 |
| #20290222 | 2 |
| #20290040 | 2 |
| #20289585 | 2 |
| #20289560 | 2 |
| C2×#16810816 | 2 |
| #9253 | 53 |