Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1092 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20244229 | C2 | semidirect |
| 2. #20242123 | C2 | semidirect |
| 3. #20241980 | C2 | semidirect |
| 4. #20241827 | C2 | semidirect |
| 6. #15689147 | C22 | semidirect |
| 8. C4×#10625329 | C22 | semidirect |
| 134. Q8×C47 | #100 | semidirect |
| 150. D4×C47 | #100 | semidirect |
| 221. C47 | #8469 | semidirect |
| 331. Q8 | #13093941 | semidirect |
| 347. D4 | #13093941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244229 | 2 |
| #20242123 | 2 |
| #20241980 | 2 |
| #20241827 | 2 |
| C47×#3498 | 2 |
| #8469 | 47 |