Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D53 | C2 | semidirect |
| 3. #368×D53 | C2 | semidirect |
| 4. #20272906 | C2 | semidirect |
| 5. #20272905 | C2 | semidirect |
| 6. #20272904 | C2 | semidirect |
| 7. C53×#1419 | C2 | semidirect |
| 17. #16810457 | C22 | semidirect |
| 20. #16810453 | C22 | semidirect |
| 23. C53×M64 | C22 | semidirect |
| 24. C53×#368 | C22 | semidirect |
| 126. #1419 | D53 | direct (N × H) |
| 132. D53 | #1419 | direct (N × H) |
| 145. M64 | C2×D53 | semidirect |
| 149. #368 | C2×D53 | semidirect |
| 150. C53 | C2×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| M64×D53 | 2 |
| #368×D53 | 2 |
| #20272906 | 2 |
| #20272905 | 2 |
| #20272904 | 2 |
| C53×#1419 | 2 |
| C2×#1419 | 53 |