Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×D424 | C2 | semidirect |
| 2. C2×#16811061 | C2 | semidirect |
| 3. #20284296 | C2 | semidirect |
| 4. #20276646 | C2 | semidirect |
| 5. #20276629 | C2 | semidirect |
| 6. #20276432 | C2 | semidirect |
| 7. C53×#2112 | C2 | semidirect |
| 9. C2×#13133239 | C22 | semidirect |
| 17. C2×#13133162 | C22 | semidirect |
| 18. C2×D848 | C22 | semidirect |
| 19. #16810864 | C22 | semidirect |
| 20. #16810859 | C22 | semidirect |
| 22. #16810661 | C22 | semidirect |
| 24. #16810425 | C22 | semidirect |
| 26. C2×M32×C53 | C22 | semidirect |
| 27. C53×C22⋊C16 | C22 | semidirect |
| 37. C2×Dic212 | C23 | semidirect |
| 45. C2×D424 | D4 | semidirect |
| 47. C2×D424 | C23 | semidirect |
| 56. #13133151 | C23 | semidirect |
| 67. C2×C16×C53 | C23 | semidirect |
| 159. C22×C53 | #509 | semidirect |
| 179. #2112 | D53 | semidirect |
| 198. C2×M32 | C2×D53 | semidirect |
| 205. C22⋊C16 | C2×D53 | semidirect |
| 206. C53 | #33517 | semidirect |
| 242. C2×C16 | C22×D53 | semidirect |
| 343. C22 | #16811061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D424 | 2 |
| C2×#16811061 | 2 |
| #20284296 | 2 |
| #20276646 | 2 |
| #20276629 | 2 |
| #20276432 | 2 |
| C53×#2112 | 2 |
| #33517 | 53 |