Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20245191 | C2 | semidirect |
| 3. #20241396 | C2 | semidirect |
| 4. C4×#106×C47 | C2 | semidirect |
| 6. #15689528 | C4 | semidirect |
| 7. #15689500 | C4 | semidirect |
| 12. C4×D376 | C4 | semidirect |
| 123. C4×#106 | D47 | semidirect |
| 145. C47 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253967 | 2 |
| #20245191 | 2 |
| #20241396 | 2 |
| C4×#106×C47 | 2 |
| #11744 | 47 |