Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×#13133156 | C2 | semidirect |
| 2. C2×#16810856 | C2 | semidirect |
| 3. #20276815 | C2 | direct (N × H) |
| 4. C2×#16810451 | C2 | semidirect |
| 5. C2×#16810424 | C2 | semidirect |
| 6. C22×D16×C53 | C2 | semidirect |
| 10. C2×#13133156 | C22 | semidirect |
| 13. #16810856 | C22 | semidirect |
| 16. #16810451 | C22 | semidirect |
| 17. #16810424 | C22 | semidirect |
| 20. C2×D16×C53 | C22 | semidirect |
| 46. C2×C16×C53 | D4 | semidirect |
| 78. C16×C53 | C2×D4 | semidirect |
| 123. C22×D16 | D53 | semidirect |
| 130. C2×C53 | #2218 | semidirect |
| 138. C2×D16 | C2×D53 | semidirect |
| 149. C53 | C2×#2218 | semidirect |
| 171. C2×C16 | C22⋊D53 | semidirect |
| 207. C16 | C2×C22⋊D53 | semidirect |
| 252. C2 | #20276815 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133156 | 2 |
| C2×#16810856 | 2 |
| #20276815 | 2 |
| C2×#16810451 | 2 |
| C2×#16810424 | 2 |
| C22×D16×C53 | 2 |
| C2×#2218 | 53 |