Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #20276935 | C2 | direct (N × H) |
| 4. C2×#16810446 | C2 | semidirect |
| 5. C2×#16810440 | C2 | semidirect |
| 18. #16810446 | C22 | semidirect |
| 19. #16810440 | C22 | semidirect |
| 148. C2×C53 | #2239 | semidirect |
| 166. C53 | C2×#2239 | semidirect |
| 285. C2 | #20276935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810881 | 2 |
| C2×#16810672 | 2 |
| #20276935 | 2 |
| C2×#16810446 | 2 |
| C2×#16810440 | 2 |
| C2×C53×#349 | 2 |
| C2×#2239 | 53 |