Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #20241991 | C2 | semidirect |
| 5. #20241745 | C2 | semidirect |
| 6. #20241238 | C2 | semidirect |
| 7. C47×#1290 | C2 | semidirect |
| 202. #1290 | D47 | semidirect |
| 236. C47 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689424 | 2 |
| #20252425 | 2 |
| #20241991 | 2 |
| #20241830 | 2 |
| #20241745 | 2 |
| #20241238 | 2 |
| C47×#1290 | 2 |
| #9245 | 47 |