Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #20275543 | C2 | semidirect |
| 3. C4×#13133128 | C2 | semidirect |
| 4. #20273470 | C2 | semidirect |
| 5. #20273166 | C2 | semidirect |
| 6. #20273165 | C2 | semidirect |
| 7. C53×#1962 | C2 | semidirect |
| 9. #16811026 | C4 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 12. #16810969 | C4 | semidirect |
| 149. #88322 | #104 | semidirect |
| 173. #1962 | D53 | semidirect |
| 203. C53 | #9849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285290 | 2 |
| #20275543 | 2 |
| C4×#13133128 | 2 |
| #20273470 | 2 |
| #20273166 | 2 |
| #20273165 | 2 |
| C53×#1962 | 2 |
| #9849 | 53 |