Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4⋊C16×D47 | C2 | semidirect |
| 3. #334×D47 | C2 | semidirect |
| 4. #20241432 | C2 | semidirect |
| 5. #20241431 | C2 | semidirect |
| 6. #20241430 | C2 | semidirect |
| 7. C47×#1360 | C2 | semidirect |
| 20. C4⋊(C47⋊C16) | C22 | semidirect |
| 22. #15688874 | C22 | semidirect |
| 25. C47×C4⋊C16 | C22 | semidirect |
| 26. C47×#334 | C22 | semidirect |
| 179. #1360 | D47 | direct (N × H) |
| 185. D47 | #1360 | direct (N × H) |
| 201. C4⋊C16 | C2×D47 | semidirect |
| 204. #334 | C2×D47 | semidirect |
| 205. C47 | C2×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D47 | 2 |
| C4⋊C16×D47 | 2 |
| #334×D47 | 2 |
| #20241432 | 2 |
| #20241431 | 2 |
| #20241430 | 2 |
| C47×#1360 | 2 |
| C2×#1360 | 47 |