Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×#15689473 | C2 | semidirect |
| 4. #20242990 | C2 | direct (N × H) |
| 5. C2×C8×C47⋊C8 | C2 | semidirect |
| 6. C2×C47×#498 | C2 | semidirect |
| 13. #15689473 | C22 | semidirect |
| 19. C8×C47⋊C8 | C22 | semidirect |
| 22. C47×#498 | C22 | semidirect |
| 122. C2×#498 | D47 | semidirect |
| 128. C2×C47 | #1708 | semidirect |
| 137. #498 | C2×D47 | semidirect |
| 150. C47 | C2×#1708 | semidirect |
| 248. C2 | #20242990 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689496 | 2 |
| C2×#15689473 | 2 |
| C2×#15689471 | 2 |
| #20242990 | 2 |
| C2×C8×C47⋊C8 | 2 |
| C2×C47×#498 | 2 |
| C2×#1708 | 47 |