Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#16811359 | C2 | semidirect |
| 2. C2×#16810820 | C2 | semidirect |
| 3. #20273772 | C2 | direct (N × H) |
| 4. C2×#16810367 | C2 | semidirect |
| 5. C2×#16810355 | C2 | semidirect |
| 10. #16811359 | C22 | semidirect |
| 16. #16810820 | C22 | semidirect |
| 19. #16810367 | C22 | semidirect |
| 20. #16810355 | C22 | semidirect |
| 168. C2×C53 | #1620 | semidirect |
| 191. C53 | C2×#1620 | semidirect |
| 326. C2 | #20273772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811359 | 2 |
| C2×#16810820 | 2 |
| #20273772 | 2 |
| C2×#16810367 | 2 |
| C2×#16810355 | 2 |
| C2×C53×#493 | 2 |
| C2×#1620 | 53 |