Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
684 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 15. #16810519 | C4 | semidirect |
| 16. #16810493 | C4 | semidirect |
| 19. C2×C4⋊Q8×C53 | C4 | semidirect |
| 29. (C2×#6157)⋊C4 | Q8 | semidirect |
| 186. C2×C4⋊Q8 | #6157 | semidirect |
| 201. C53 | #9909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290570 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| #20289588 | 2 |
| #20283062 | 2 |
| #9909 | 53 |