Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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×#11719923 | C2 | semidirect |
| 2. C23×#11719922 | C2 | semidirect |
| 3. C22×#13133205 | C2 | semidirect |
| 4. C2×#16811010 | C2 | direct (N × H) |
| 5. C22×#13133128 | C2 | semidirect |
| 6. C22×#127×C53 | C2 | semidirect |
| 10. C22×#11719923 | C22 | semidirect |
| 12. C22×#11719922 | C22 | semidirect |
| 15. C2×#13133205 | C22 | semidirect |
| 17. #16811010 | C22 | direct (N × H) |
| 18. C2×#13133128 | C22 | semidirect |
| 22. C2×#127×C53 | C22 | semidirect |
| 33. C2×#11719923 | C23 | semidirect |
| 35. C2×#11719922 | C23 | semidirect |
| 36. C22×#88322 | D4 | semidirect |
| 39. #13133205 | C23 | semidirect |
| 41. #13133128 | C23 | semidirect |
| 52. #127×C53 | C23 | semidirect |
| 89. C2×#88322 | C2×D4 | semidirect |
| 118. #88322 | C22×D4 | semidirect |
| 123. C22×C53 | #496 | semidirect |
| 136. C22×#127 | D53 | semidirect |
| 141. C2×C53 | C2×#496 | semidirect |
| 155. C2×#127 | C2×D53 | semidirect |
| 162. C53 | C22×#496 | semidirect |
| 187. #127 | C22×D53 | semidirect |
| 264. C22 | #16811010 | direct (N × H) |
| 274. C2 | C2×#16811010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719923 | 2 |
| C23×#11719922 | 2 |
| C22×#13133205 | 2 |
| C2×#16811010 | 2 |
| C22×#13133128 | 2 |
| C22×#127×C53 | 2 |
| C22×#496 | 53 |