Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20242114 | C2 | semidirect |
| 5. #20241900 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#3139 | C2 | semidirect |
| 176. #3139 | D47 | semidirect |
| 210. C47 | #10098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254387 | 2 |
| #20249329 | 2 |
| #20242114 | 2 |
| #20241985 | 2 |
| #20241900 | 2 |
| #20241282 | 2 |
| C47×#3139 | 2 |
| #10098 | 47 |