Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 219 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×#15689758 | C2 | semidirect |
| 2. C2×#15689315 | C2 | semidirect |
| 3. #20242440 | C2 | direct (N × H) |
| 4. C2×#15688867 | C2 | semidirect |
| 5. C2×#15688852 | C2 | semidirect |
| 6. C2×C47×#493 | C2 | semidirect |
| 11. #15689758 | C22 | semidirect |
| 16. #15689315 | C22 | semidirect |
| 17. C2×C4⋊(C47⋊C8) | C22 | semidirect |
| 19. #15688867 | C22 | semidirect |
| 20. #15688852 | C22 | semidirect |
| 23. C2×#127×C47 | C22 | semidirect |
| 25. C47×#493 | C22 | semidirect |
| 26. C2×C4×C8×C47 | C22 | semidirect |
| 50. C4⋊(C47⋊C8) | C23 | semidirect |
| 64. #127×C47 | C23 | semidirect |
| 67. C4×C8×C47 | C23 | semidirect |
| 98. C2×D188 | D8 | semidirect |
| 154. D188 | C2×D8 | semidirect |
| 182. C2×#493 | D47 | semidirect |
| 189. C2×C47 | #1619 | semidirect |
| 200. C2×#127 | C2×D47 | semidirect |
| 205. #493 | C2×D47 | semidirect |
| 210. C2×C4×C8 | C2×D47 | semidirect |
| 213. C47 | C2×#1619 | semidirect |
| 237. #127 | C22×D47 | semidirect |
| 254. C4×C8 | C22×D47 | semidirect |
| 370. C2 | #20242440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689758 | 2 |
| C2×#15689315 | 2 |
| #20242440 | 2 |
| C2×#15688867 | 2 |
| C2×#15688852 | 2 |
| C2×C47×#493 | 2 |
| C2×#1619 | 47 |