Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
538 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 538 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. #20243455 | C2 | semidirect |
| 3. #20243145 | C2 | semidirect |
| 4. #20241213 | C2 | semidirect |
| 5. #20241213 | C2 | semidirect |
| 6. #20241209 | C2 | semidirect |
| 7. C47×#1270 | C2 | semidirect |
| 222. #1270 | D47 | semidirect |
| 251. C47 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251688 | 2 |
| #20243455 | 2 |
| #20243145 | 2 |
| #20241213 | 2 |
| #20241209 | 2 |
| C47×#1270 | 2 |
| #7670 | 47 |