Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20252305 | C2 | semidirect |
| 2. C2×#15688936 | C2 | semidirect |
| 3. #20245116 | C2 | semidirect |
| 4. #20244299 | C2 | semidirect |
| 5. #20241492 | C2 | semidirect |
| 6. #20241473 | C2 | semidirect |
| 24. C2×SD32×C47 | C4 | semidirect |
| 25. C2×D16×C47 | C4 | semidirect |
| 183. C2×SD32 | Dic47 | semidirect |
| 184. C2×D16 | Dic47 | semidirect |
| 197. C47 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252305 | 2 |
| C2×#15688936 | 2 |
| #20245116 | 2 |
| #20244299 | 2 |
| #20241492 | 2 |
| #20241473 | 2 |
| C2×C47×#509 | 2 |
| #13036 | 47 |