Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
312 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20291056 | C2 | semidirect |
| 4. #20290926 | C2 | semidirect |
| 5. #20289770 | C2 | semidirect |
| 6. #20289766 | C2 | semidirect |
| 166. C53 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291056 | 2 |
| #20290957 | 2 |
| C2×#16811521 | 2 |
| #20290926 | 2 |
| #20289770 | 2 |
| #20289766 | 2 |
| #20274518 | 2 |
| #13123 | 53 |