Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#16810401 | C2 | semidirect |
| 5. #20272823 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C53×#1943 | C2 | semidirect |
| 15. #16810426 | C4 | semidirect |
| 16. #16810423 | C4 | semidirect |
| 147. #1943 | D53 | semidirect |
| 171. C53 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810432 | 2 |
| #20276425 | 2 |
| C2×#16810401 | 2 |
| #20275608 | 2 |
| #20272823 | 2 |
| #20272813 | 2 |
| C53×#1943 | 2 |
| #13153 | 53 |