Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20251996 | C2 | semidirect |
| 3. C2×#15688937 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20245017 | C2 | semidirect |
| 6. #20241499 | C2 | semidirect |
| 7. C47×#1385 | C2 | semidirect |
| 169. #1385 | D47 | semidirect |
| 194. C47 | #13007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689394 | 2 |
| #20251996 | 2 |
| C2×#15688937 | 2 |
| C2×#15688935 | 2 |
| #20245017 | 2 |
| #20241499 | 2 |
| C47×#1385 | 2 |
| #13007 | 47 |