Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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×#16811021 | C2 | semidirect |
| 3. C2×#16810974 | C2 | semidirect |
| 5. #20274316 | C2 | direct (N × H) |
| 6. C2×C82×C53 | C2 | semidirect |
| 12. #16811021 | C22 | semidirect |
| 16. #16810974 | C22 | semidirect |
| 24. C82×C53 | C22 | semidirect |
| 127. C2×C82 | D53 | semidirect |
| 128. C2×C53 | #1708 | semidirect |
| 149. C82 | C2×D53 | semidirect |
| 150. C53 | C2×#1708 | semidirect |
| 248. C2 | #20274316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811021 | 2 |
| C2×#16810996 | 2 |
| C2×#16810974 | 2 |
| C2×#16810970 | 2 |
| #20274316 | 2 |
| C2×C82×C53 | 2 |
| C2×#1708 | 53 |