Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20252458 | C2 | semidirect |
| 3. #20242102 | C2 | semidirect |
| 4. #20242022 | C2 | semidirect |
| 5. #20241261 | C2 | semidirect |
| 6. #20241259 | C2 | semidirect |
| 7. C47×#1555 | C2 | semidirect |
| 161. #1555 | D47 | semidirect |
| 188. C47 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253838 | 2 |
| #20252458 | 2 |
| #20242102 | 2 |
| #20242022 | 2 |
| #20241261 | 2 |
| #20241259 | 2 |
| C47×#1555 | 2 |
| #9423 | 47 |