Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1138 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×#15689871 | C2 | semidirect |
| 2. C2×#15689510 | C2 | semidirect |
| 3. #20242680 | C2 | direct (N × H) |
| 4. C2×#15688865 | C2 | semidirect |
| 5. C2×#15688862 | C2 | semidirect |
| 6. C2×C47×#490 | C2 | semidirect |
| 11. #15689871 | C22 | semidirect |
| 17. #15689510 | C22 | semidirect |
| 19. #15688865 | C22 | semidirect |
| 20. #15688862 | C22 | semidirect |
| 24. C47×#490 | C22 | semidirect |
| 159. C2×#490 | D47 | semidirect |
| 164. C2×C47 | #1656 | semidirect |
| 182. #490 | C2×D47 | semidirect |
| 188. C47 | C2×#1656 | semidirect |
| 320. C2 | #20242680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689871 | 2 |
| C2×#15689510 | 2 |
| #20242680 | 2 |
| C2×#15688865 | 2 |
| C2×#15688862 | 2 |
| C2×C47×#490 | 2 |
| C2×#1656 | 47 |