Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
398 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #20241281 | C2 | semidirect |
| 5. #20241252 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#2605 | C2 | semidirect |
| 29. #13094024 | Q8 | semidirect |
| 30. #13094021 | Q8 | semidirect |
| 176. #2605 | D47 | semidirect |
| 208. C47 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244306 | 2 |
| #20241934 | 2 |
| #20241895 | 2 |
| #20241281 | 2 |
| #20241252 | 2 |
| #20241244 | 2 |
| C47×#2605 | 2 |
| #10378 | 47 |