Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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. C2×#16811229 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. #20280466 | C2 | semidirect |
| 4. #20275712 | C2 | semidirect |
| 5. #20275681 | C2 | semidirect |
| 6. #20275539 | C2 | semidirect |
| 7. #20275060 | C2 | semidirect |
| 8. #20274484 | C2 | semidirect |
| 9. C2×C53×#490 | C2 | semidirect |
| 46. #13133214 | D4 | semidirect |
| 74. #125×C53 | D4 | semidirect |
| 203. C2×#490 | D53 | semidirect |
| 242. C53 | #25608 | semidirect |
| 261. #125 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811229 | 2 |
| C2×#16810999 | 2 |
| #20280466 | 2 |
| #20275712 | 2 |
| #20275681 | 2 |
| #20275539 | 2 |
| #20275060 | 2 |
| #20274484 | 2 |
| C2×C53×#490 | 2 |
| #25608 | 53 |