Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1190 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×#16810425 | C2 | semidirect |
| 3. #20274744 | C2 | semidirect |
| 4. C2×C53×C22⋊C16 | C2 | semidirect |
| 9. C22×D424 | C4 | semidirect |
| 11. C2×#13133151 | C22 | semidirect |
| 16. C22×C16×C53 | C22 | semidirect |
| 81. D424 | C22⋊C4 | semidirect |
| 123. C22×C53 | #357 | semidirect |
| 142. C2×C22⋊C16 | D53 | semidirect |
| 158. C22×C16 | C2×D53 | semidirect |
| 164. C53 | #12731 | semidirect |
| 275. C22 | #16810425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D424 | 2 |
| C2×#16810425 | 2 |
| #20274744 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #12731 | 53 |