Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D188 | C2 | semidirect |
| 2. #20245637 | C2 | semidirect |
| 3. #20242740 | C2 | semidirect |
| 4. #20241435 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. #20241342 | C2 | semidirect |
| 7. C47×#2206 | C2 | semidirect |
| 17. C4×C47⋊C16 | C22 | semidirect |
| 18. #15688876 | C22 | semidirect |
| 21. C47×#493 | C22 | semidirect |
| 23. C47×C4⋊C16 | C22 | semidirect |
| 77. D8×C47 | D8 | semidirect |
| 126. D188 | D16 | semidirect |
| 158. #2206 | D47 | semidirect |
| 175. #493 | C2×D47 | semidirect |
| 182. C4⋊C16 | C2×D47 | semidirect |
| 187. C47 | #12316 | semidirect |
| 245. D8 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D188 | 2 |
| #20245637 | 2 |
| #20242740 | 2 |
| #20241435 | 2 |
| #20241349 | 2 |
| #20241342 | 2 |
| C47×#2206 | 2 |
| #12316 | 47 |