Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16811064 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. C2×#16810431 | C2 | semidirect |
| 5. #20275631 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C22×SD32×C53 | C2 | semidirect |
| 53. #13133157 | D4 | semidirect |
| 68. C2×Q16×C53 | D4 | semidirect |
| 79. C2×C16×C53 | D4 | semidirect |
| 197. C22×SD32 | D53 | semidirect |
| 232. C53 | #13338 | semidirect |
| 248. C2×Q16 | C22⋊D53 | semidirect |
| 275. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20285196 | 2 |
| C2×#16810436 | 2 |
| C2×#16810431 | 2 |
| #20275631 | 2 |
| #20272803 | 2 |
| C22×SD32×C53 | 2 |
| #13338 | 53 |