Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1310 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 232 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×#16811645 | C2 | semidirect |
| 2. #20290195 | C2 | direct (N × H) |
| 3. C2×#16811479 | C2 | semidirect |
| 4. C2×#16811478 | C2 | semidirect |
| 7. #16811645 | C22 | semidirect |
| 10. C2×#13133272 | C22 | semidirect |
| 11. #16811479 | C22 | semidirect |
| 12. #16811478 | C22 | semidirect |
| 29. #13133272 | C23 | semidirect |
| 196. C2×C53 | #1533 | semidirect |
| 220. C53 | C2×#1533 | semidirect |
| 388. C2 | #20290195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811645 | 2 |
| #20290195 | 2 |
| C2×#16811479 | 2 |
| C2×#16811478 | 2 |
| C2×#124×D53 | 2 |
| C2×#1533 | 53 |