Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1258 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 231 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. #20251868 | C2 | semidirect |
| 3. #20243932 | C2 | semidirect |
| 4. #20243803 | C2 | semidirect |
| 5. #20243500 | C2 | semidirect |
| 6. #20243316 | C2 | semidirect |
| 7. C47×#1785 | C2 | semidirect |
| 191. #1785 | D47 | semidirect |
| 220. C47 | #21781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257046 | 2 |
| #20251868 | 2 |
| #20243932 | 2 |
| #20243803 | 2 |
| #20243500 | 2 |
| #20243316 | 2 |
| C47×#1785 | 2 |
| #21781 | 47 |