Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
674 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20249750 | C2 | semidirect |
| 2. #20244459 | C2 | semidirect |
| 3. #20244459 | C2 | semidirect |
| 4. #20241211 | C2 | semidirect |
| 5. #20241208 | C2 | semidirect |
| 6. #20241208 | C2 | semidirect |
| 7. C47×#2041 | C2 | semidirect |
| 110. C2×D188 | D8 | semidirect |
| 121. C4⋊C4×C47 | D8 | semidirect |
| 253. #2041 | D47 | semidirect |
| 288. C47 | #7737 | semidirect |
| 394. C4⋊C4 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20249750 | 2 |
| #20244459 | 2 |
| #20241211 | 2 |
| #20241208 | 2 |
| C47×#2041 | 2 |
| #7737 | 47 |