Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245613 | C2 | semidirect |
| 2. #20245428 | C2 | semidirect |
| 4. #20241446 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. C47×#3338 | C2 | semidirect |
| 92. D4×C47 | SD32 | semidirect |
| 130. #3338 | D47 | semidirect |
| 159. C47 | #12342 | semidirect |
| 232. D4 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245613 | 2 |
| #20245428 | 2 |
| #20242743 | 2 |
| #20241446 | 2 |
| #20241352 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#3338 | 2 |
| #12342 | 47 |