Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20252023 | C2 | semidirect |
| 3. #20244234 | C2 | semidirect |
| 4. #20244226 | C2 | semidirect |
| 5. #20243314 | C2 | semidirect |
| 6. #20243309 | C2 | semidirect |
| 7. C47×#1783 | C2 | semidirect |
| 16. #15689146 | C22 | semidirect |
| 17. C2×#13093942 | C22 | semidirect |
| 19. C2×#13093940 | C22 | semidirect |
| 21. M16×Dic47 | C22 | semidirect |
| 159. #1783 | D47 | semidirect |
| 183. C47 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689690 | 2 |
| #20252023 | 2 |
| #20244234 | 2 |
| #20244226 | 2 |
| #20243314 | 2 |
| #20243309 | 2 |
| C47×#1783 | 2 |
| #21801 | 47 |