Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20275666 | C2 | semidirect |
| 4. #20273440 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1290 | C2 | semidirect |
| 10. #16811032 | C4 | semidirect |
| 11. #16810983 | C4 | semidirect |
| 188. #1290 | D53 | semidirect |
| 221. C53 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285938 | 2 |
| #20283851 | 2 |
| #20275666 | 2 |
| #20273440 | 2 |
| #20273241 | 2 |
| #20272570 | 2 |
| C53×#1290 | 2 |
| #9375 | 53 |