Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
878 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20285512 | C2 | semidirect |
| 2. C2×#16810757 | C2 | semidirect |
| 3. #20274636 | C2 | semidirect |
| 4. #20273075 | C2 | semidirect |
| 5. #20273074 | C2 | semidirect |
| 6. #20272603 | C2 | semidirect |
| 7. C2×C53×#447 | C2 | semidirect |
| 234. C2×#447 | D53 | semidirect |
| 271. C53 | #9986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| C2×#16810757 | 2 |
| #20274636 | 2 |
| #20273075 | 2 |
| #20273074 | 2 |
| #20272603 | 2 |
| C2×C53×#447 | 2 |
| #9986 | 53 |