Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20244564 | C2 | semidirect |
| 3. #20243120 | C2 | semidirect |
| 4. C47×#3458 | C2 | semidirect |
| 19. C22×Dic94 | Q8 | semidirect |
| 20. C22×D188 | Q8 | semidirect |
| 22. C22×C4×D47 | Q8 | semidirect |
| 128. #3458 | D47 | semidirect |
| 147. C47 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689096 | 2 |
| #20244564 | 2 |
| #20243120 | 2 |
| C47×#3458 | 2 |
| #23474 | 47 |