Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#16810449 | C2 | semidirect |
| 3. #20272894 | C2 | direct (N × H) |
| 4. C22×C32×C53 | C2 | semidirect |
| 8. C2×D848 | C4 | semidirect |
| 12. #16810449 | C22 | semidirect |
| 15. C2×C32×C53 | C22 | semidirect |
| 24. D848 | C2×C4 | semidirect |
| 83. C22×C32 | D53 | semidirect |
| 86. C2×C53 | #1415 | semidirect |
| 99. C2×C32 | C2×D53 | semidirect |
| 102. C53 | C2×#1415 | semidirect |
| 169. C2 | #20272894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810449 | 2 |
| #20272894 | 2 |
| C22×C32×C53 | 2 |
| C2×#1415 | 53 |