Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #20245668 | C2 | semidirect |
| 3. #20245665 | C2 | semidirect |
| 4. #20245663 | C2 | semidirect |
| 7. C47×#2252 | C2 | semidirect |
| 35. C16×D47 | Q8 | semidirect |
| 110. #2252 | D47 | semidirect |
| 133. C47 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253899 | 2 |
| #20245668 | 2 |
| #20245665 | 2 |
| #20245663 | 2 |
| #20245169 | 2 |
| C4×C16×D47 | 2 |
| C47×#2252 | 2 |
| #33726 | 47 |