Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20289120 | C2 | semidirect |
| 2. #20286093 | C2 | semidirect |
| 3. #20273858 | C2 | semidirect |
| 4. #20273829 | C2 | semidirect |
| 5. #20273796 | C2 | semidirect |
| 6. #20273767 | C2 | semidirect |
| 7. #20273450 | C2 | semidirect |
| 8. #20273167 | C2 | semidirect |
| 9. C53×#3147 | C2 | semidirect |
| 19. #16810910 | C22 | semidirect |
| 22. #16810815 | C22 | semidirect |
| 23. #16810647 | C22 | semidirect |
| 24. #16810372 | C22 | semidirect |
| 26. #16810352 | C22 | semidirect |
| 27. #16810352 | C22 | semidirect |
| 30. C53×#532 | C22 | semidirect |
| 32. C53×#494 | C22 | semidirect |
| 35. C53×#492 | C22 | semidirect |
| 36. C2×C4×C8×C53 | C22 | semidirect |
| 202. #3147 | D53 | semidirect |
| 225. #532 | C2×D53 | semidirect |
| 227. #494 | C2×D53 | semidirect |
| 230. #492 | C2×D53 | semidirect |
| 237. C2×C4×C8 | C2×D53 | semidirect |
| 242. C53 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20286093 | 2 |
| #20273858 | 2 |
| #20273829 | 2 |
| #20273796 | 2 |
| #20273767 | 2 |
| #20273450 | 2 |
| #20273167 | 2 |
| C53×#3147 | 2 |
| #18686 | 53 |