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. #20242086 | C2 | semidirect |
| 3. #20242081 | C2 | semidirect |
| 4. #20242002 | C2 | semidirect |
| 5. #20241998 | C2 | semidirect |
| 6. #20241729 | C2 | semidirect |
| 7. C47×#1955 | C2 | semidirect |
| 218. #1955 | 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 |
|---|---|
| #20257240 | 2 |
| #20242086 | 2 |
| #20242081 | 2 |
| #20242002 | 2 |
| #20241998 | 2 |
| #20241729 | 2 |
| C47×#1955 | 2 |
| #8458 | 47 |