Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20276504 | C2 | semidirect |
| 3. C2×#16810449 | C2 | semidirect |
| 6. #20272825 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 21. #16810406 | C4 | semidirect |
| 42. #13133157 | C2×C4 | semidirect |
| 57. C2×C16×C53 | C2×C4 | semidirect |
| 158. #1382 | D53 | semidirect |
| 183. C53 | #12925 | semidirect |
| 207. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283312 | 2 |
| #20276504 | 2 |
| C2×#16810449 | 2 |
| C2×#16810406 | 2 |
| #20274776 | 2 |
| #20272825 | 2 |
| C53×#1382 | 2 |
| #12925 | 53 |