Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 530 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. #20290849 | C2 | semidirect |
| 2. #20290848 | C2 | semidirect |
| 3. C4×#13133271 | C2 | semidirect |
| 4. #20290271 | C2 | semidirect |
| 5. #20290062 | C2 | semidirect |
| 6. #20290061 | C2 | semidirect |
| 20. #16811026 | C4 | semidirect |
| 21. #16810999 | C4 | semidirect |
| 22. #16810970 | C4 | semidirect |
| 26. C53×#486 | C4 | semidirect |
| 149. #88322 | #104 | semidirect |
| 189. #486 | #6157 | semidirect |
| 203. C53 | #9849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290849 | 2 |
| #20290848 | 2 |
| C4×#13133271 | 2 |
| #20290271 | 2 |
| #20290062 | 2 |
| #20290061 | 2 |
| #20285293 | 2 |
| #9849 | 53 |