Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#16811515 | C2 | semidirect |
| 5. #20289766 | C2 | semidirect |
| 6. #20289762 | C2 | semidirect |
| 161. C53 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291056 | 2 |
| #20290957 | 2 |
| #20290951 | 2 |
| C2×#16811515 | 2 |
| #20289766 | 2 |
| #20289762 | 2 |
| #20274560 | 2 |
| #13127 | 53 |