Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 25. #16810370 | C4 | semidirect |
| 26. #16810369 | C4 | semidirect |
| 27. #16810368 | C4 | semidirect |
| 28. C53×#332 | C4 | semidirect |
| 177. #332 | #6157 | semidirect |
| 178. C53 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291626 | 2 |
| #20290900 | 2 |
| #20290293 | 2 |
| #20289542 | 2 |
| #20273378 | 2 |
| #8936 | 53 |