Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15688920 | C2 | semidirect |
| 2. C2×#15688918 | C2 | semidirect |
| 3. #20241545 | C2 | direct (N × H) |
| 8. #15688920 | C22 | semidirect |
| 10. #15688918 | C22 | semidirect |
| 13. C2×#127×C47 | C4 | semidirect |
| 17. C47×#496 | C4 | semidirect |
| 19. C2×#97×C47 | C4 | semidirect |
| 41. #127×C47 | C2×C4 | semidirect |
| 50. #97×C47 | C2×C4 | semidirect |
| 163. C2×C47 | #1406 | semidirect |
| 167. C2×#127 | Dic47 | semidirect |
| 171. #496 | Dic47 | semidirect |
| 175. C2×#97 | Dic47 | semidirect |
| 180. C47 | C2×#1406 | semidirect |
| 197. #127 | C2×Dic47 | semidirect |
| 211. #97 | C2×Dic47 | semidirect |
| 319. C2 | #20241545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688920 | 2 |
| C2×#15688918 | 2 |
| #20241545 | 2 |
| C2×C47×#496 | 2 |
| C2×#1406 | 47 |