Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 4. C2×#16810400 | C2 | semidirect |
| 5. #20274623 | C2 | semidirect |
| 6. #20272828 | C2 | semidirect |
| 7. C53×#1385 | C2 | semidirect |
| 17. #16810438 | C4 | semidirect |
| 18. #16810435 | C4 | semidirect |
| 19. #16810431 | C4 | semidirect |
| 146. #1385 | D53 | semidirect |
| 169. C53 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810744 | 2 |
| #20276462 | 2 |
| #20276444 | 2 |
| C2×#16810400 | 2 |
| #20274623 | 2 |
| #20272828 | 2 |
| C53×#1385 | 2 |
| #12651 | 53 |