Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 500 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. Q8×#11719936 | C2 | semidirect |
| 3. C4×#13133280 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289546 | C2 | semidirect |
| 25. #16810905 | C4 | semidirect |
| 26. #16810824 | C4 | semidirect |
| 27. #16810823 | C4 | semidirect |
| 32. C53×#475 | C4 | semidirect |
| 118. #11719936 | SD16 | semidirect |
| 152. Q8×C53 | #104 | semidirect |
| 232. #475 | #6157 | semidirect |
| 253. C53 | #8992 | semidirect |
| 373. Q8 | #13133282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719936 | 2 |
| #20290878 | 2 |
| C4×#13133280 | 2 |
| #20290062 | 2 |
| #20289612 | 2 |
| #20289546 | 2 |
| #20284748 | 2 |
| #8992 | 53 |