Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C2×#16810416 | C2 | semidirect |
| 3. #20272877 | C2 | direct (N × H) |
| 4. C2×C53×#353 | C2 | semidirect |
| 7. C2×#13133214 | C4 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 13. C2×C4×#88322 | C4 | semidirect |
| 15. #16810416 | C22 | semidirect |
| 19. C53×#353 | C22 | semidirect |
| 33. #13133214 | C2×C4 | semidirect |
| 38. C4×#88322 | C2×C4 | semidirect |
| 168. C2×#353 | D53 | semidirect |
| 176. C2×C53 | #1408 | semidirect |
| 193. #353 | C2×D53 | semidirect |
| 194. C53 | C2×#1408 | semidirect |
| 347. C2 | #20272877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| C2×#16810416 | 2 |
| #20272877 | 2 |
| C2×C53×#353 | 2 |
| C2×#1408 | 53 |