Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#16811064 | C2 | semidirect |
| 3. #20276665 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20276336 | C2 | semidirect |
| 6. C53×#3059 | C2 | semidirect |
| 16. #16811064 | C22 | semidirect |
| 19. C2×#13133157 | C22 | semidirect |
| 20. #16810432 | C22 | semidirect |
| 21. #16810405 | C22 | semidirect |
| 22. C22×Q16×C53 | C22 | semidirect |
| 25. C53×#470 | C22 | semidirect |
| 27. C53×#427 | C22 | semidirect |
| 195. #3059 | D53 | semidirect |
| 212. C22×Q16 | C2×D53 | semidirect |
| 220. #470 | C2×D53 | semidirect |
| 222. #427 | C2×D53 | semidirect |
| 226. C53 | #33532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289489 | 2 |
| C2×#16811064 | 2 |
| #20276665 | 2 |
| #20276450 | 2 |
| #20276336 | 2 |
| C53×#3059 | 2 |
| #33532 | 53 |