Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
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×D47 | C2 | semidirect |
| 3. #368×D47 | C2 | semidirect |
| 4. #20241579 | C2 | semidirect |
| 5. #20241578 | C2 | semidirect |
| 6. #20241577 | C2 | semidirect |
| 7. C47×#1419 | C2 | semidirect |
| 17. #15688957 | C22 | semidirect |
| 20. #15688953 | C22 | semidirect |
| 23. C47×M64 | C22 | semidirect |
| 24. C47×#368 | C22 | semidirect |
| 126. #1419 | D47 | direct (N × H) |
| 132. D47 | #1419 | direct (N × H) |
| 145. M64 | C2×D47 | semidirect |
| 149. #368 | C2×D47 | semidirect |
| 150. C47 | C2×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D47 | 2 |
| M64×D47 | 2 |
| #368×D47 | 2 |
| #20241579 | 2 |
| #20241578 | 2 |
| #20241577 | 2 |
| C47×#1419 | 2 |
| C2×#1419 | 47 |