Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20244215 | C2 | semidirect |
| 3. C4×C8×Dic47 | C2 | semidirect |
| 4. #20241838 | C2 | semidirect |
| 5. C47×#1567 | C2 | semidirect |
| 7. #15689528 | C4 | semidirect |
| 8. #15689500 | C4 | semidirect |
| 9. #15689470 | C4 | semidirect |
| 75. C4×Dic47 | D8 | semidirect |
| 104. C8×C47 | #104 | semidirect |
| 126. #1567 | D47 | semidirect |
| 147. C47 | #9844 | semidirect |
| 233. C8 | #13093950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253967 | 2 |
| #20244215 | 2 |
| C4×C8×Dic47 | 2 |
| #20241838 | 2 |
| C47×#1567 | 2 |
| #9844 | 47 |