Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#15688937 | C2 | semidirect |
| 3. #20245116 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. #20244992 | C2 | semidirect |
| 6. #20243511 | C2 | semidirect |
| 7. C47×#2145 | C2 | semidirect |
| 13. #15689508 | C4 | semidirect |
| 14. #15689498 | C4 | semidirect |
| 47. C2×C47⋊C16 | D4 | semidirect |
| 63. M32×C47 | D4 | semidirect |
| 171. #2145 | D47 | semidirect |
| 201. C47 | #13215 | semidirect |
| 233. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253875 | 2 |
| C2×#15688937 | 2 |
| #20245116 | 2 |
| #20245103 | 2 |
| #20244992 | 2 |
| #20243511 | 2 |
| C47×#2145 | 2 |
| #13215 | 47 |