Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #20272916 | C2 | semidirect |
| 4. #20272914 | C2 | semidirect |
| 7. #16810457 | C4 | semidirect |
| 20. #13133123 | C2×C4 | semidirect |
| 86. C53 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810457 | 2 |
| #20276499 | 2 |
| #20272916 | 2 |
| #20272914 | 2 |
| C2×C53×#366 | 2 |
| #13634 | 53 |