Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
864 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20244217 | C2 | semidirect |
| 2. C4×#13093951 | C2 | semidirect |
| 3. #20241980 | C2 | semidirect |
| 4. #20241827 | C2 | semidirect |
| 15. Q82×C47 | C4 | semidirect |
| 18. C47×#555 | C4 | semidirect |
| 20. C47×#550 | C4 | semidirect |
| 135. Q8×C47 | #104 | semidirect |
| 200. Q82 | Dic47 | semidirect |
| 203. #555 | Dic47 | semidirect |
| 205. #550 | Dic47 | semidirect |
| 220. C47 | #8441 | semidirect |
| 330. Q8 | #13093951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244217 | 2 |
| C4×#13093951 | 2 |
| #20241980 | 2 |
| #20241827 | 2 |
| C47×#3483 | 2 |
| #8441 | 47 |