Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×D376 | C2 | semidirect |
| 2. #20245637 | C2 | semidirect |
| 3. #20245420 | C2 | semidirect |
| 4. #20241433 | C2 | semidirect |
| 5. #20241348 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. C47×#1667 | C2 | semidirect |
| 17. C4⋊(C47⋊C16) | C22 | semidirect |
| 19. C4×C47⋊C16 | C22 | semidirect |
| 20. C47×#493 | C22 | semidirect |
| 23. C47×#335 | C22 | semidirect |
| 94. D376 | D8 | semidirect |
| 110. D4×C47 | D16 | semidirect |
| 159. #1667 | D47 | semidirect |
| 175. #493 | C2×D47 | semidirect |
| 185. #335 | C2×D47 | semidirect |
| 187. C47 | #12316 | semidirect |
| 282. D4 | #13093965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D376 | 2 |
| #20245637 | 2 |
| #20245420 | 2 |
| #20241433 | 2 |
| #20241348 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#1667 | 2 |
| #12316 | 47 |