Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 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×#15689539 | C2 | semidirect |
| 2. #20253032 | C2 | semidirect |
| 3. #20245488 | C2 | semidirect |
| 4. #20245471 | C2 | semidirect |
| 5. #20245172 | C2 | semidirect |
| 6. #20245104 | C2 | semidirect |
| 7. C22×D16×C47 | C2 | semidirect |
| 12. C2×#13093963 | C22 | semidirect |
| 13. C2×C16×D47 | C22 | semidirect |
| 15. #15689356 | C22 | semidirect |
| 18. #15688951 | C22 | semidirect |
| 19. #15688949 | C22 | semidirect |
| 20. #15688924 | C22 | semidirect |
| 52. C2×C16×C47 | D4 | semidirect |
| 125. C22×D16 | D47 | semidirect |
| 155. C47 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689539 | 2 |
| #20253032 | 2 |
| #20245488 | 2 |
| #20245471 | 2 |
| #20245172 | 2 |
| #20245104 | 2 |
| C22×D16×C47 | 2 |
| #33607 | 47 |