Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20275891 | C2 | semidirect |
| 3. #20274447 | C2 | semidirect |
| 4. C53×#3458 | C2 | semidirect |
| 19. C22×Dic106 | Q8 | semidirect |
| 20. C22×D212 | Q8 | semidirect |
| 22. C22×C4×D53 | Q8 | semidirect |
| 128. #3458 | D53 | semidirect |
| 147. C53 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810596 | 2 |
| #20275891 | 2 |
| #20274447 | 2 |
| C53×#3458 | 2 |
| #23474 | 53 |