Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1220 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20283179 | C2 | semidirect |
| 3. #20276386 | C2 | semidirect |
| 4. #20276378 | C2 | semidirect |
| 5. C53×#2884 | C2 | semidirect |
| 6. C2×#13133263 | C4 | semidirect |
| 11. #16811197 | C4 | semidirect |
| 14. C2×#13133206 | C4 | semidirect |
| 16. #41×Dic53 | C4 | semidirect |
| 18. #16810597 | C22 | semidirect |
| 19. #16810417 | C22 | semidirect |
| 20. #16810415 | C22 | semidirect |
| 24. C53×#410 | C22 | semidirect |
| 178. #2884 | D53 | semidirect |
| 203. #410 | C2×D53 | semidirect |
| 206. C53 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288509 | 2 |
| #20283179 | 2 |
| #20276386 | 2 |
| #20276378 | 2 |
| C53×#2884 | 2 |
| #33362 | 53 |