Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×Dic424 | C2 | semidirect |
| 3. #20272916 | C2 | semidirect |
| 4. #20272895 | C2 | semidirect |
| 6. C4×#13133123 | C2 | semidirect |
| 10. #16810461 | C4 | direct (N × H) |
| 23. Dic424 | C2×C4 | semidirect |
| 27. #13133123 | C2×C4 | semidirect |
| 77. C4×C53 | SD64 | semidirect |
| 105. C53 | C4×SD64 | semidirect |
| 164. C4 | #16810461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810461 | 2 |
| C4×Dic424 | 2 |
| #20272916 | 2 |
| #20272895 | 2 |
| #20272893 | 2 |
| C4×#13133123 | 2 |
| C4×D16×C53 | 2 |
| C4×SD64 | 53 |