Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275634 | C2 | semidirect |
| 3. C4×#13133148 | C2 | semidirect |
| 4. #20273210 | C2 | semidirect |
| 5. #20273209 | C2 | semidirect |
| 6. #20273002 | C2 | semidirect |
| 7. C53×#1980 | C2 | semidirect |
| 9. #16811026 | C4 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 12. #16810969 | C4 | semidirect |
| 171. #88322 | #104 | semidirect |
| 197. #1980 | D53 | semidirect |
| 232. C53 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285290 | 2 |
| #20275634 | 2 |
| C4×#13133148 | 2 |
| #20273210 | 2 |
| #20273209 | 2 |
| #20273002 | 2 |
| C53×#1980 | 2 |
| #9721 | 53 |