Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 578 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×#11719936 | C2 | semidirect |
| 2. #20290879 | C2 | semidirect |
| 3. C4×#13133279 | C2 | semidirect |
| 4. #20290061 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289546 | C2 | semidirect |
| 25. #16810904 | C4 | semidirect |
| 26. #16810903 | C4 | semidirect |
| 27. #16810815 | C4 | semidirect |
| 32. C53×#459 | C4 | semidirect |
| 130. #11719936 | D8 | semidirect |
| 169. D4×C53 | #104 | semidirect |
| 263. #459 | #6157 | semidirect |
| 281. C53 | #8991 | semidirect |
| 422. D4 | #13133281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719936 | 2 |
| #20290879 | 2 |
| C4×#13133279 | 2 |
| #20290061 | 2 |
| #20289612 | 2 |
| #20289546 | 2 |
| #20284714 | 2 |
| #8991 | 53 |