Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1126 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×#15689853 | C2 | semidirect |
| 3. #20242464 | C2 | direct (N × H) |
| 4. C2×#15688872 | C2 | semidirect |
| 5. C2×#15688855 | C2 | semidirect |
| 10. #15689853 | C22 | semidirect |
| 19. #15688872 | C22 | semidirect |
| 20. #15688855 | C22 | semidirect |
| 86. C2×Dic94 | SD16 | semidirect |
| 134. Dic94 | C2×SD16 | semidirect |
| 159. C2×C47 | #1623 | semidirect |
| 182. C47 | C2×#1623 | semidirect |
| 308. C2 | #20242464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689853 | 2 |
| C2×#15689320 | 2 |
| #20242464 | 2 |
| C2×#15688872 | 2 |
| C2×#15688855 | 2 |
| C2×C47×#492 | 2 |
| C2×#1623 | 47 |