Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244185 | C2 | semidirect |
| 3. #20242081 | C2 | semidirect |
| 4. #20242003 | C2 | semidirect |
| 5. #20242000 | C2 | semidirect |
| 6. #20241728 | C2 | semidirect |
| 7. C47×#1552 | C2 | semidirect |
| 219. #1552 | D47 | semidirect |
| 255. C47 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257242 | 2 |
| #20244185 | 2 |
| #20242081 | 2 |
| #20242003 | 2 |
| #20242000 | 2 |
| #20241728 | 2 |
| C47×#1552 | 2 |
| #8458 | 47 |