Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20253941 | C2 | semidirect |
| 3. #20253211 | C2 | semidirect |
| 4. #20249331 | C2 | semidirect |
| 5. #20244601 | C2 | semidirect |
| 6. #20244227 | C2 | semidirect |
| 7. #20243599 | C2 | semidirect |
| 8. #20243199 | C2 | semidirect |
| 9. C47×#1995 | C2 | semidirect |
| 138. #10625329 | #41 | semidirect |
| 200. #1995 | D47 | semidirect |
| 236. C47 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257265 | 2 |
| #20253941 | 2 |
| #20253211 | 2 |
| #20249331 | 2 |
| #20244601 | 2 |
| #20244227 | 2 |
| #20243599 | 2 |
| #20243199 | 2 |
| C47×#1995 | 2 |
| #25690 | 47 |