Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1066 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20291279 | C2 | semidirect |
| 3. C2×#16811504 | C2 | semidirect |
| 4. #20290421 | C2 | semidirect |
| 9. #16811593 | C4 | semidirect |
| 121. C2×#88324 | C22⋊C4 | semidirect |
| 245. C53 | #10937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811593 | 2 |
| #20291279 | 2 |
| C2×#16811504 | 2 |
| #20290421 | 2 |
| #20277093 | 2 |
| #10937 | 53 |