Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #20254771 | C2 | semidirect |
| 3. #20244366 | C2 | semidirect |
| 4. #20244217 | C2 | semidirect |
| 5. #20244215 | C2 | semidirect |
| 6. C47⋊#1309 | C2 | semidirect |
| 7. C47×#3254 | C2 | semidirect |
| 214. #3254 | D47 | semidirect |
| 251. C47 | #10301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20254766 | 2 |
| #20244366 | 2 |
| #20244217 | 2 |
| #20244215 | 2 |
| C47⋊#1309 | 2 |
| C47×#3254 | 2 |
| #10301 | 47 |