Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
604 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×Q8×#6157 | C2 | semidirect |
| 4. #20290044 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 25. #16810905 | C4 | semidirect |
| 26. #16810824 | C4 | semidirect |
| 27. #16810823 | C4 | semidirect |
| 32. C53×#475 | C4 | semidirect |
| 123. C4×#6157 | SD16 | semidirect |
| 163. Q8×C53 | #104 | semidirect |
| 195. Dic106 | #104 | semidirect |
| 244. #475 | #6157 | semidirect |
| 264. C53 | #9234 | semidirect |
| 389. Q8 | #13133282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×#6157 | 2 |
| #20290848 | 2 |
| #20290096 | 2 |
| #20290044 | 2 |
| #20289612 | 2 |
| #20289542 | 2 |
| #20284748 | 2 |
| #9234 | 53 |