Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
872 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 224 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. #20290206 | C2 | semidirect |
| 4. #20290179 | C2 | semidirect |
| 5. #20290177 | C2 | semidirect |
| 6. #20290172 | C2 | semidirect |
| 193. C53 | #17692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291561 | 2 |
| #20290206 | 2 |
| #20290179 | 2 |
| #20290177 | 2 |
| #20290172 | 2 |
| #20288537 | 2 |
| #17692 | 53 |