Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 228 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. #20290244 | C2 | semidirect |
| 3. #20290236 | C2 | semidirect |
| 12. #16811482 | C22 | semidirect |
| 186. C53 | #17755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811643 | 2 |
| #20290244 | 2 |
| #20290236 | 2 |
| C2×#16811176 | 2 |
| #17755 | 53 |