Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20283775 | C2 | semidirect |
| 3. #20273272 | C2 | semidirect |
| 4. #20273245 | C2 | semidirect |
| 5. #20273074 | C2 | semidirect |
| 6. #20272624 | C2 | semidirect |
| 7. C53×#1293 | C2 | semidirect |
| 10. #16810954 | C4 | semidirect |
| 12. #16810937 | C4 | semidirect |
| 15. #16810776 | C4 | semidirect |
| 17. #16810759 | C4 | semidirect |
| 224. #1293 | D53 | semidirect |
| 260. C53 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285531 | 2 |
| #20283775 | 2 |
| #20273272 | 2 |
| #20273245 | 2 |
| #20273074 | 2 |
| #20272624 | 2 |
| C53×#1293 | 2 |
| #9332 | 53 |