Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20245181 | C2 | semidirect |
| 3. #20241595 | C2 | semidirect |
| 4. #20241594 | C2 | semidirect |
| 5. #20241578 | C2 | semidirect |
| 6. #20241527 | C2 | semidirect |
| 7. C47×#1419 | C2 | semidirect |
| 85. #1419 | D47 | semidirect |
| 102. C47 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245488 | 2 |
| #20245181 | 2 |
| #20241595 | 2 |
| #20241594 | 2 |
| #20241578 | 2 |
| #20241527 | 2 |
| C47×#1419 | 2 |
| #13717 | 47 |