Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20289927 | C2 | semidirect |
| 4. #20289917 | C2 | semidirect |
| 5. #20289601 | C2 | semidirect |
| 6. #20289601 | C2 | semidirect |
| 193. C53 | #8245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291440 | 2 |
| #20290171 | 2 |
| #20289927 | 2 |
| #20289917 | 2 |
| #20289601 | 2 |
| #20273376 | 2 |
| #8245 | 53 |