Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 17. #16810398 | C4 | semidirect |
| 18. #16810398 | C4 | semidirect |
| 19. C4×#11719908 | C4 | semidirect |
| 20. C4×C16×C53 | C4 | semidirect |
| 125. C4×C16 | #6157 | semidirect |
| 126. C53 | #12904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811548 | 2 |
| C2×#16811547 | 2 |
| #20290655 | 2 |
| #20290652 | 2 |
| C4×#13133156 | 2 |
| #12904 | 53 |