Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×D848 | C2 | semidirect |
| 2. C22×#13133158 | C2 | semidirect |
| 3. C2×#16810998 | C2 | semidirect |
| 4. #20276963 | C2 | direct (N × H) |
| 5. C2×C16×Dic53 | C2 | semidirect |
| 6. C22×D16×C53 | C2 | semidirect |
| 11. C2×D848 | C22 | semidirect |
| 13. C2×#13133158 | C22 | semidirect |
| 16. #16810998 | C22 | semidirect |
| 18. C16×Dic53 | C22 | semidirect |
| 21. C2×D16×C53 | C22 | semidirect |
| 37. C2×#11719908 | D4 | semidirect |
| 48. C2×C16×C53 | D4 | semidirect |
| 79. C16×C53 | C2×D4 | semidirect |
| 80. #11719908 | C2×D4 | semidirect |
| 96. C2×Dic53 | D16 | semidirect |
| 118. Dic53 | C2×D16 | semidirect |
| 121. C22×D16 | D53 | semidirect |
| 126. C2×C53 | #2246 | semidirect |
| 139. C2×D16 | C2×D53 | semidirect |
| 146. C53 | C2×#2246 | semidirect |
| 170. C2×C16 | C22⋊D53 | semidirect |
| 204. C16 | C2×C22⋊D53 | semidirect |
| 244. C2 | #20276963 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C22×#13133158 | 2 |
| C2×#16810998 | 2 |
| #20276963 | 2 |
| C2×C16×Dic53 | 2 |
| C22×D16×C53 | 2 |
| C2×#2246 | 53 |