Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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. #20252382 | C2 | semidirect |
| 3. #20241998 | C2 | semidirect |
| 4. #20241947 | C2 | semidirect |
| 5. #20241924 | C2 | semidirect |
| 6. #20241287 | C2 | semidirect |
| 7. C47×#1295 | C2 | semidirect |
| 10. #15689532 | C4 | semidirect |
| 11. #15689512 | C4 | semidirect |
| 12. #15689488 | C4 | semidirect |
| 13. #15689483 | C4 | semidirect |
| 208. #1295 | D47 | semidirect |
| 243. C47 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254086 | 2 |
| #20252382 | 2 |
| #20241998 | 2 |
| #20241947 | 2 |
| #20241924 | 2 |
| #20241287 | 2 |
| C47×#1295 | 2 |
| #9432 | 47 |