Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C22×#13133292 | C2 | semidirect |
| 2. C2×#16811540 | C2 | semidirect |
| 3. #20290591 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 17. #16810861 | C4 | semidirect |
| 18. #16810860 | C4 | semidirect |
| 19. #16810859 | C4 | semidirect |
| 24. C53×#467 | C4 | semidirect |
| 29. #13133292 | D4 | semidirect |
| 157. C22×C53 | #360 | semidirect |
| 198. #467 | #6157 | semidirect |
| 209. C53 | #13065 | semidirect |
| 351. C22 | #16811540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133292 | 2 |
| C2×#16811540 | 2 |
| #20290591 | 2 |
| #20289786 | 2 |
| #20284298 | 2 |
| #13065 | 53 |