Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20275691 | C2 | semidirect |
| 4. C4×#13133127 | C2 | semidirect |
| 5. #20273169 | C2 | semidirect |
| 7. C53×#1567 | C2 | semidirect |
| 10. #16811021 | C4 | semidirect |
| 11. #16810996 | C4 | semidirect |
| 12. #16810974 | C4 | semidirect |
| 13. #16810970 | C4 | semidirect |
| 140. C8×C53 | #104 | semidirect |
| 165. #1567 | D53 | semidirect |
| 192. C53 | #9851 | semidirect |
| 307. C8 | #13133143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285274 | 2 |
| #20275691 | 2 |
| #20275542 | 2 |
| C4×#13133127 | 2 |
| #20273169 | 2 |
| #20273165 | 2 |
| C53×#1567 | 2 |
| #9851 | 53 |