Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#16811057 | C2 | semidirect |
| 2. #20285142 | C2 | semidirect |
| 3. #493×D53 | C2 | semidirect |
| 4. #20276978 | C2 | semidirect |
| 5. #20276971 | C2 | semidirect |
| 6. #20276970 | C2 | semidirect |
| 7. #20276964 | C2 | semidirect |
| 8. C4×#13133156 | C2 | semidirect |
| 9. C53×#2246 | C2 | semidirect |
| 17. C2×#13133162 | C22 | semidirect |
| 18. C2×#13133161 | C22 | semidirect |
| 19. C2×#13133158 | C22 | semidirect |
| 22. #16811006 | C22 | semidirect |
| 23. #16811003 | C22 | semidirect |
| 30. #16810398 | C22 | semidirect |
| 31. C4×#11719908 | C22 | semidirect |
| 32. C2×D16×C53 | C22 | semidirect |
| 34. C53×#493 | C22 | semidirect |
| 35. C4×C16×C53 | C22 | semidirect |
| 64. #13133156 | D4 | semidirect |
| 120. C16×C53 | C2×D4 | semidirect |
| 121. #11719908 | C2×D4 | semidirect |
| 166. C4×C53 | #509 | semidirect |
| 179. #2246 | D53 | semidirect |
| 197. C2×D16 | C2×D53 | semidirect |
| 207. #493 | C2×D53 | semidirect |
| 212. C4×C16 | C2×D53 | semidirect |
| 213. C53 | #33717 | semidirect |
| 299. C16 | D4×D53 | semidirect |
| 346. C4 | #16811057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811057 | 2 |
| #20285142 | 2 |
| #493×D53 | 2 |
| #20276978 | 2 |
| #20276971 | 2 |
| #20276970 | 2 |
| #20276964 | 2 |
| C4×#13133156 | 2 |
| C53×#2246 | 2 |
| #33717 | 53 |