Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20245274 | C2 | semidirect |
| 2. #20245264 | C2 | semidirect |
| 3. #20241594 | C2 | semidirect |
| 4. #20241578 | C2 | semidirect |
| 5. #20241575 | C2 | semidirect |
| 6. #20241523 | C2 | semidirect |
| 18. C47×SD64 | C4 | semidirect |
| 19. C47×D32 | C4 | semidirect |
| 32. Q32×C47 | C2×C4 | semidirect |
| 36. D16×C47 | C2×C4 | semidirect |
| 38. C32×C47 | C2×C4 | semidirect |
| 99. SD64 | Dic47 | semidirect |
| 100. D32 | Dic47 | semidirect |
| 108. C47 | #13658 | semidirect |
| 113. Q32 | C2×Dic47 | semidirect |
| 117. D16 | C2×Dic47 | semidirect |
| 126. C32 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245274 | 2 |
| #20245264 | 2 |
| #20241594 | 2 |
| #20241578 | 2 |
| #20241575 | 2 |
| #20241523 | 2 |
| C47×#2263 | 2 |
| #13658 | 47 |