Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2270 conjugacy classes of subgroups.
The subgroup lattice has 546 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20243099 | C2 | direct (N × H) |
| 4. C2×#15688884 | C2 | semidirect |
| 12. C2×#13093983 | C4 | semidirect |
| 13. C2×#13093983 | C4 | semidirect |
| 14. C2×#13093983 | C4 | semidirect |
| 19. C22×C4⋊Dic47 | C4 | semidirect |
| 24. #15688884 | C22 | semidirect |
| 29. C22×M16×C47 | C4 | semidirect |
| 45. #13093983 | C2×C4 | semidirect |
| 46. #13093983 | C2×C4 | semidirect |
| 53. C2×C4⋊Dic47 | C2×C4 | semidirect |
| 66. C2×C4×Dic47 | C2×C4 | semidirect |
| 89. C2×M16×C47 | C2×C4 | semidirect |
| 90. C2×M16×C47 | C2×C4 | semidirect |
| 154. M16×C47 | C22×C4 | semidirect |
| 171. C4×Dic47 | C22×C4 | semidirect |
| 275. C2×C47 | #1733 | semidirect |
| 282. C22×M16 | Dic47 | semidirect |
| 305. C47 | C2×#1733 | semidirect |
| 329. C2×M16 | C2×Dic47 | semidirect |
| 330. C2×M16 | C2×Dic47 | semidirect |
| 427. M16 | C22×Dic47 | semidirect |
| 542. C2 | #20243099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093983 | 2 |
| #20243099 | 2 |
| C2×#15688884 | 2 |
| C23×M16×C47 | 2 |
| C2×#1733 | 47 |