Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20244164 | C2 | semidirect |
| 3. #20242141 | C2 | semidirect |
| 6. #20241262 | C2 | semidirect |
| 7. C47×#1570 | C2 | semidirect |
| 154. #1570 | D47 | semidirect |
| 182. C47 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244227 | 2 |
| #20244164 | 2 |
| #20242141 | 2 |
| #20242055 | 2 |
| C2×#15688866 | 2 |
| #20241262 | 2 |
| C47×#1570 | 2 |
| #10607 | 47 |