Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 3. #20241562 | C2 | semidirect |
| 4. #20241547 | C2 | semidirect |
| 6. #15689735 | C4 | semidirect |
| 8. #15689495 | C4 | semidirect |
| 9. #15689487 | C4 | semidirect |
| 15. #15689184 | C4 | semidirect |
| 28. #13094024 | C2×C4 | semidirect |
| 30. #13094016 | C2×C4 | semidirect |
| 42. #13093935 | C2×C4 | semidirect |
| 43. C4×C47⋊C8 | C2×C4 | semidirect |
| 175. C47 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254460 | 2 |
| #20245080 | 2 |
| #20241562 | 2 |
| #20241547 | 2 |
| C47×#2127 | 2 |
| #13607 | 47 |