Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
514 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 75 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×#15688920 | C2 | semidirect |
| 3. #20241537 | C2 | direct (N × H) |
| 4. C2×C47×#329 | C2 | semidirect |
| 15. #15688920 | C22 | semidirect |
| 19. C47×#329 | C22 | semidirect |
| 174. C2×#329 | D47 | semidirect |
| 180. C2×C47 | #1403 | semidirect |
| 197. #329 | C2×D47 | semidirect |
| 198. C47 | C2×#1403 | semidirect |
| 355. C2 | #20241537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689300 | 2 |
| C2×#15688920 | 2 |
| #20241537 | 2 |
| C2×C47×#329 | 2 |
| C2×#1403 | 47 |