Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 98 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. D53⋊(C22⋊C16) | C2 | semidirect |
| 2. C2×#16811497 | C2 | semidirect |
| 3. #20289702 | C2 | semidirect |
| 4. #20289701 | C2 | semidirect |
| 8. #16811518 | C22 | semidirect |
| 11. #16811497 | C22 | semidirect |
| 12. C2×D8×D53 | C4 | semidirect |
| 16. #16810859 | C4 | semidirect |
| 20. #107×D53 | C4 | semidirect |
| 22. C53×#466 | C4 | semidirect |
| 33. C2×D424 | C2×C4 | semidirect |
| 49. #13133151 | C2×C4 | semidirect |
| 54. C2×D8×C53 | C2×C4 | semidirect |
| 57. #107×C53 | C2×C4 | semidirect |
| 198. D53 | #1347 | semidirect |
| 209. #466 | #6157 | semidirect |
| 216. C53 | C2×#1347 | semidirect |
| 224. C2×D8 | C2×#6157 | semidirect |
| 248. #107 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| C2×#16811497 | 2 |
| #20289702 | 2 |
| #20289701 | 2 |
| #466×D53 | 2 |
| C2×#1347 | 53 |