Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20245571 | C2 | semidirect |
| 2. #20245566 | C2 | semidirect |
| 3. #20244828 | C2 | semidirect |
| 4. #20241403 | C2 | semidirect |
| 5. #20241403 | C2 | semidirect |
| 6. #20241314 | C2 | semidirect |
| 8. C2×#13093958 | C22 | semidirect |
| 14. C22⋊(C47⋊C16) | C22 | semidirect |
| 15. C22⋊(C47⋊C16) | C22 | semidirect |
| 17. #15688888 | C22 | semidirect |
| 190. C47 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245571 | 2 |
| #20245566 | 2 |
| #20244828 | 2 |
| #20241403 | 2 |
| #20241314 | 2 |
| C47×#3199 | 2 |
| #12284 | 47 |