Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 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. #20241558 | C2 | semidirect |
| 4. #20241552 | C2 | semidirect |
| 6. #15689735 | C4 | semidirect |
| 7. #15689518 | C4 | semidirect |
| 10. #15689477 | C4 | semidirect |
| 15. #15689184 | C4 | semidirect |
| 27. #13094024 | C2×C4 | semidirect |
| 29. #13094016 | C2×C4 | semidirect |
| 42. #13093935 | C2×C4 | semidirect |
| 43. C4×C47⋊C8 | C2×C4 | semidirect |
| 176. C47 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254460 | 2 |
| #20245060 | 2 |
| #20241558 | 2 |
| #20241552 | 2 |
| C47×#2127 | 2 |
| #13610 | 47 |