Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16810428 | C2 | semidirect |
| 9. C22×Dic212 | C4 | semidirect |
| 78. Dic212 | C22⋊C4 | semidirect |
| 113. C22×C53 | #358 | semidirect |
| 148. C53 | #12732 | semidirect |
| 243. C22 | #16810428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic212 | 2 |
| C2×#16810428 | 2 |
| #20274744 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #12732 | 53 |