Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
546 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20250347 | C2 | semidirect |
| 2. #20244619 | C2 | semidirect |
| 3. #20244619 | C2 | semidirect |
| 4. #20241212 | C2 | semidirect |
| 5. #20241210 | C2 | semidirect |
| 6. #20241209 | C2 | semidirect |
| 116. C4⋊Dic47 | D8 | semidirect |
| 257. C47 | #7740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20250347 | 2 |
| #20244619 | 2 |
| #20241212 | 2 |
| #20241210 | 2 |
| #20241209 | 2 |
| C47×#2011 | 2 |
| #7740 | 47 |