Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1220 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 311 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. #20251852 | C2 | semidirect |
| 2. #20245060 | C2 | semidirect |
| 3. #20245053 | C2 | semidirect |
| 7. #15689097 | C22 | semidirect |
| 8. #15688918 | C22 | semidirect |
| 9. #15688916 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C47 | C4 | semidirect |
| 14. C47×#536 | C4 | semidirect |
| 17. C2×#124×C47 | C4 | semidirect |
| 18. C4×#41×C47 | C4 | semidirect |
| 143. C2×H(5,𝔽2) | Dic47 | semidirect |
| 146. #536 | Dic47 | semidirect |
| 149. C2×#124 | Dic47 | semidirect |
| 151. C4×#41 | Dic47 | semidirect |
| 156. C47 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251852 | 2 |
| #20245060 | 2 |
| #20245053 | 2 |
| C47×#3500 | 2 |
| #33362 | 47 |