Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20245125 | C2 | semidirect |
| 3. #20245096 | C2 | semidirect |
| 4. #20243434 | C2 | semidirect |
| 5. C47×#2113 | C2 | semidirect |
| 11. #15689923 | C4 | semidirect |
| 14. #15689161 | C22 | semidirect |
| 21. C2×M32×C47 | C22 | semidirect |
| 22. C22×C16×C47 | C22 | semidirect |
| 166. #2113 | D47 | semidirect |
| 182. C2×M32 | C2×D47 | semidirect |
| 183. C22×C16 | C2×D47 | semidirect |
| 191. C47 | #12745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258162 | 2 |
| #20245125 | 2 |
| #20245096 | 2 |
| #20243434 | 2 |
| C47×#2113 | 2 |
| #12745 | 47 |