Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 384 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×Dic188 | C2 | semidirect |
| 2. #20245644 | C2 | semidirect |
| 3. #20245429 | C2 | semidirect |
| 5. #20241438 | C2 | semidirect |
| 6. #20241353 | C2 | semidirect |
| 7. C47×D4⋊C16 | C2 | semidirect |
| 89. Dic188 | D8 | semidirect |
| 98. D4×C47 | SD32 | semidirect |
| 147. D4⋊C16 | D47 | semidirect |
| 170. C47 | #12318 | semidirect |
| 254. D4 | #13093969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic188 | 2 |
| #20245644 | 2 |
| #20245429 | 2 |
| #20242743 | 2 |
| #20241438 | 2 |
| #20241353 | 2 |
| C47×D4⋊C16 | 2 |
| #12318 | 47 |