Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20244368 | C2 | semidirect |
| 4. #20241953 | C2 | semidirect |
| 5. #20241248 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 10. #15689495 | C4 | semidirect |
| 11. #15689469 | C4 | semidirect |
| 29. #13094024 | C2×C4 | semidirect |
| 30. #13094024 | C2×C4 | semidirect |
| 48. C4×C47⋊C8 | C2×C4 | semidirect |
| 116. C4×Dic47 | SD16 | semidirect |
| 221. C47 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254329 | 2 |
| #20246114 | 2 |
| #20244368 | 2 |
| #20241953 | 2 |
| #20241248 | 2 |
| #20241216 | 2 |
| C47×#1545 | 2 |
| #9295 | 47 |