Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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⋊M64 | C2 | semidirect |
| 2. C2×#16811550 | C2 | semidirect |
| 3. #20289869 | C2 | semidirect |
| 4. #20289868 | C2 | semidirect |
| 7. #16811556 | C22 | semidirect |
| 11. #16811550 | C22 | semidirect |
| 14. #16811055 | C4 | semidirect |
| 18. Q32×D53 | C4 | semidirect |
| 20. D16×D53 | C4 | semidirect |
| 22. C53×#508 | C4 | semidirect |
| 37. Dic424 | C2×C4 | semidirect |
| 42. D848 | C2×C4 | semidirect |
| 50. Q32×C53 | C2×C4 | semidirect |
| 52. D16×C53 | C2×C4 | semidirect |
| 142. D53 | #1418 | semidirect |
| 149. #508 | #6157 | semidirect |
| 160. C53 | C2×#1418 | semidirect |
| 175. Q32 | C2×#6157 | semidirect |
| 182. D16 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| C2×#16811550 | 2 |
| #20289869 | 2 |
| #20289868 | 2 |
| #508×D53 | 2 |
| C2×#1418 | 53 |