Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20252107 | C2 | semidirect |
| 3. #20242038 | C2 | semidirect |
| 4. #20241813 | C2 | semidirect |
| 5. #20241285 | C2 | semidirect |
| 6. #20241233 | C2 | semidirect |
| 7. C47×#1955 | C2 | semidirect |
| 105. C2×C8×C47 | D8 | semidirect |
| 203. #1955 | D47 | semidirect |
| 236. C47 | #9049 | semidirect |
| 321. C2×C8 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253388 | 2 |
| #20252107 | 2 |
| #20242038 | 2 |
| #20241813 | 2 |
| #20241285 | 2 |
| #20241233 | 2 |
| C47×#1955 | 2 |
| #9049 | 47 |