Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20245560 | C2 | semidirect |
| 3. #20245559 | C2 | semidirect |
| 4. #20243021 | C2 | semidirect |
| 5. #20241426 | C2 | semidirect |
| 6. #20241365 | C2 | semidirect |
| 7. C47×#1336 | C2 | semidirect |
| 164. #1336 | D47 | semidirect |
| 188. C47 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255193 | 2 |
| #20245560 | 2 |
| #20245559 | 2 |
| #20243021 | 2 |
| #20241426 | 2 |
| #20241365 | 2 |
| C47×#1336 | 2 |
| #12367 | 47 |