Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1382 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 267 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. #20283350 | C2 | semidirect |
| 3. #20274796 | C2 | semidirect |
| 4. #20274705 | C2 | semidirect |
| 6. #100×Dic53 | C2 | semidirect |
| 16. #16810646 | C22 | semidirect |
| 19. M16×Dic53 | C22 | semidirect |
| 20. #16810391 | C22 | semidirect |
| 166. C53 | #20729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811098 | 2 |
| #20283350 | 2 |
| #20274796 | 2 |
| #20274705 | 2 |
| #20274636 | 2 |
| #100×Dic53 | 2 |
| C53×#1783 | 2 |
| #20729 | 53 |