Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 564 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. #20272861 | C2 | direct (N × H) |
| 4. C2×C53×#331 | C2 | semidirect |
| 5. C2×#13133262 | C4 | semidirect |
| 9. #16810790 | C4 | semidirect |
| 12. C2×#13133134 | C4 | semidirect |
| 15. #16810416 | C22 | semidirect |
| 19. C53×#331 | C22 | semidirect |
| 23. #13133262 | C2×C4 | semidirect |
| 38. #13133134 | C2×C4 | semidirect |
| 191. C2×#331 | D53 | semidirect |
| 199. C2×C53 | #1402 | semidirect |
| 216. #331 | C2×D53 | semidirect |
| 217. C53 | C2×#1402 | semidirect |
| 393. C2 | #20272861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810790 | 2 |
| C2×#16810416 | 2 |
| #20272861 | 2 |
| C2×C53×#331 | 2 |
| C2×#1402 | 53 |