Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1506 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 180 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×#13133281 | C2 | semidirect |
| 2. #20290379 | C2 | semidirect |
| 3. C4×(C2×#6157)⋊C4 | C2 | semidirect |
| 14. C2×#13133217 | C4 | semidirect |
| 15. C2×#13133204 | C4 | semidirect |
| 19. C2×#127×C53 | C4 | semidirect |
| 24. C2×#11719936 | D4 | semidirect |
| 29. C2×C4×#6157 | D4 | semidirect |
| 138. C2×C4×C53 | #104 | semidirect |
| 205. C2×#127 | #6157 | semidirect |
| 216. C53 | #11011 | semidirect |
| 356. C2×C4 | #13133281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133281 | 2 |
| #20290379 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| C2×#16811171 | 2 |
| #11011 | 53 |