Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 3. #20245493 | C2 | direct (N × H) |
| 4. C2×#15688951 | C2 | semidirect |
| 5. C2×#15688927 | C2 | semidirect |
| 6. C22×Q32×C47 | C2 | semidirect |
| 16. #15688951 | C22 | semidirect |
| 17. #15688927 | C22 | semidirect |
| 20. C2×Q32×C47 | C22 | semidirect |
| 116. C22×Q32 | D47 | semidirect |
| 122. C2×C47 | #2219 | semidirect |
| 130. C2×Q32 | C2×D47 | semidirect |
| 141. C47 | C2×#2219 | semidirect |
| 236. C2 | #20245493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093963 | 2 |
| C2×#15689361 | 2 |
| #20245493 | 2 |
| C2×#15688951 | 2 |
| C2×#15688927 | 2 |
| C22×Q32×C47 | 2 |
| C2×#2219 | 47 |