Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3350 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3350 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×#11719925 | C2 | semidirect |
| 4. C2×#16811015 | C2 | direct (N × H) |
| 5. C22×#13133128 | C2 | semidirect |
| 6. C22×C4⋊Q8×C53 | C2 | semidirect |
| 10. C22×#11719925 | C22 | semidirect |
| 17. #16811015 | C22 | direct (N × H) |
| 18. C2×#13133128 | C22 | semidirect |
| 21. C2×C4⋊Q8×C53 | C22 | semidirect |
| 33. C2×#11719925 | C23 | semidirect |
| 41. #13133128 | C23 | semidirect |
| 50. C4⋊Q8×C53 | C23 | semidirect |
| 114. C22×C53 | #497 | semidirect |
| 128. C22×C4⋊Q8 | D53 | semidirect |
| 132. C2×C53 | C2×#497 | semidirect |
| 145. C2×C4⋊Q8 | C2×D53 | semidirect |
| 153. C53 | C22×#497 | semidirect |
| 176. C4⋊Q8 | C22×D53 | semidirect |
| 246. C22 | #16811015 | direct (N × H) |
| 256. C2 | C2×#16811015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719925 | 2 |
| C23×#11719924 | 2 |
| C22×#13133205 | 2 |
| C2×#16811015 | 2 |
| C22×#13133128 | 2 |
| C22×C4⋊Q8×C53 | 2 |
| C22×#497 | 53 |