Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20249348 | C2 | direct (N × H) |
| 2. C2×#15689052 | C2 | semidirect |
| 3. C2×#15689047 | C2 | semidirect |
| 5. C2×#15689021 | C2 | semidirect |
| 6. C2×C47×#376 | C2 | semidirect |
| 12. #15689052 | C22 | semidirect |
| 13. #15689047 | C22 | semidirect |
| 15. #15689021 | C22 | semidirect |
| 18. C47×#376 | C22 | semidirect |
| 112. C2×#376 | D47 | semidirect |
| 113. C2×C47 | #2644 | semidirect |
| 128. #376 | C2×D47 | semidirect |
| 132. C47 | C2×#2644 | semidirect |
| 219. C2 | #20249348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20249348 | 2 |
| C2×#15689052 | 2 |
| C2×#15689047 | 2 |
| C2×#15689025 | 2 |
| C2×#15689021 | 2 |
| C2×C47×#376 | 2 |
| C2×#2644 | 47 |