Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20255000 | C2 | semidirect |
| 2. #20245654 | C2 | semidirect |
| 3. #20245424 | C2 | semidirect |
| 4. #20242867 | C2 | semidirect |
| 5. #20241432 | C2 | semidirect |
| 6. #20241356 | C2 | semidirect |
| 7. C47×#1330 | C2 | semidirect |
| 14. #15689500 | C22 | semidirect |
| 22. #15688874 | C22 | semidirect |
| 25. C47×C4⋊C16 | C22 | semidirect |
| 26. C47×#346 | C22 | semidirect |
| 108. D376 | D8 | semidirect |
| 179. #1330 | D47 | semidirect |
| 201. C4⋊C16 | C2×D47 | semidirect |
| 203. #346 | C2×D47 | semidirect |
| 206. C47 | #12324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255000 | 2 |
| #20245654 | 2 |
| #20245424 | 2 |
| #20242867 | 2 |
| #20241432 | 2 |
| #20241356 | 2 |
| C47×#1330 | 2 |
| #12324 | 47 |