Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
450 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 159 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. C4×#13093960 | C2 | semidirect |
| 4. #20241484 | C2 | semidirect |
| 5. C2×C4×C16×C47 | C2 | semidirect |
| 15. #15688931 | C4 | direct (N × H) |
| 34. #13093960 | C2×C4 | semidirect |
| 46. C2×C16×C47 | C2×C4 | semidirect |
| 112. C4×C47 | #359 | semidirect |
| 120. C2×C4×C16 | D47 | semidirect |
| 141. C47 | C4×#359 | semidirect |
| 160. C2×C16 | C4×D47 | semidirect |
| 235. C4 | #15688931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13094046 | 2 |
| C2×#15688931 | 2 |
| C4×#13093960 | 2 |
| #20241484 | 2 |
| C2×C4×C16×C47 | 2 |
| C4×#359 | 47 |