Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×D53⋊C32 | C2 | semidirect |
| 2. C2×#16811549 | C2 | semidirect |
| 3. #20289864 | C2 | direct (N × H) |
| 7. D53⋊C32 | C22 | semidirect |
| 10. #16811549 | C22 | semidirect |
| 12. C2×D848 | C4 | semidirect |
| 16. D16×D53 | C4 | semidirect |
| 19. C2×D16×C53 | C4 | semidirect |
| 33. D848 | C2×C4 | semidirect |
| 43. D16×C53 | C2×C4 | semidirect |
| 121. C2×C53 | #1415 | semidirect |
| 124. D53 | #1415 | semidirect |
| 134. C2×D16 | #6157 | semidirect |
| 142. C53 | C2×#1415 | semidirect |
| 158. D16 | C2×#6157 | semidirect |
| 243. C2 | #20289864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| C2×#16811549 | 2 |
| #20289864 | 2 |
| C2×D16×D53 | 2 |
| C2×#1415 | 53 |