Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 366 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 |
|---|---|---|
| 2. #20245625 | C2 | semidirect |
| 3. #20245526 | C2 | semidirect |
| 4. #20242911 | C2 | semidirect |
| 5. #20241432 | C2 | semidirect |
| 6. #20241356 | C2 | semidirect |
| 7. C47×#1330 | C2 | semidirect |
| 10. #15689528 | C22 | semidirect |
| 22. #15688874 | C22 | semidirect |
| 25. C47×C4⋊C16 | C22 | semidirect |
| 26. C47×#346 | C22 | semidirect |
| 165. #1330 | D47 | semidirect |
| 184. C4⋊C16 | C2×D47 | semidirect |
| 188. #346 | C2×D47 | semidirect |
| 191. C47 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255000 | 2 |
| #20245625 | 2 |
| #20245526 | 2 |
| #20242911 | 2 |
| #20241432 | 2 |
| #20241356 | 2 |
| C47×#1330 | 2 |
| #12376 | 47 |