Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244225 | C2 | semidirect |
| 3. #20244223 | C2 | semidirect |
| 4. #20243411 | C2 | semidirect |
| 5. #20243167 | C2 | semidirect |
| 6. #20241957 | C2 | semidirect |
| 7. C47×#1519 | C2 | semidirect |
| 8. C22×#10625334 | C4 | semidirect |
| 15. C2×#13093957 | C4 | semidirect |
| 17. C2×#13093945 | C4 | semidirect |
| 18. C2×#13093944 | C4 | semidirect |
| 202. C47⋊C8 | #99 | semidirect |
| 241. #1519 | D47 | semidirect |
| 274. C47 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689357 | 2 |
| #20244225 | 2 |
| #20244223 | 2 |
| #20243411 | 2 |
| #20243167 | 2 |
| #20241957 | 2 |
| C47×#1519 | 2 |
| #9785 | 47 |