Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20252529 | C2 | semidirect |
| 3. #20244316 | C2 | semidirect |
| 4. #20241914 | C2 | semidirect |
| 5. #20241257 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 7. C47×#1555 | C2 | semidirect |
| 9. #15689510 | C4 | semidirect |
| 10. #15689487 | C4 | semidirect |
| 212. #1555 | D47 | semidirect |
| 248. C47 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254406 | 2 |
| #20252529 | 2 |
| #20244316 | 2 |
| #20241914 | 2 |
| #20241257 | 2 |
| #20241245 | 2 |
| C47×#1555 | 2 |
| #9378 | 47 |