Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20253510 | C2 | semidirect |
| 3. #20248876 | C2 | semidirect |
| 4. #20244307 | C2 | semidirect |
| 5. #20241985 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 7. C47×#1491 | C2 | semidirect |
| 215. #1491 | D47 | semidirect |
| 249. C47 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254377 | 2 |
| #20253510 | 2 |
| #20248876 | 2 |
| #20244307 | 2 |
| #20241985 | 2 |
| #20241245 | 2 |
| C47×#1491 | 2 |
| #10006 | 47 |