Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. #20291563 | C2 | semidirect |
| 2. #20290585 | C2 | semidirect |
| 3. #20290146 | C2 | semidirect |
| 4. #20290022 | C2 | semidirect |
| 5. #20289605 | C2 | semidirect |
| 6. #20289570 | C2 | semidirect |
| 27. #16810825 | C4 | semidirect |
| 28. #16810819 | C4 | semidirect |
| 29. #16810818 | C4 | semidirect |
| 32. C53×#461 | C4 | semidirect |
| 248. #461 | #6157 | semidirect |
| 267. C53 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291563 | 2 |
| #20290585 | 2 |
| #20290146 | 2 |
| #20290022 | 2 |
| #20289605 | 2 |
| #20289570 | 2 |
| #20284180 | 2 |
| #9305 | 53 |