Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20245627 | C2 | semidirect |
| 3. #20245522 | C2 | semidirect |
| 4. #20241430 | C2 | semidirect |
| 5. #20241370 | C2 | semidirect |
| 6. #20241354 | C2 | semidirect |
| 7. C47×#1696 | C2 | semidirect |
| 145. #1696 | D47 | semidirect |
| 173. C47 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256478 | 2 |
| #20245627 | 2 |
| #20245522 | 2 |
| #20241430 | 2 |
| #20241370 | 2 |
| #20241354 | 2 |
| C47×#1696 | 2 |
| #12388 | 47 |