Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20253104 | C2 | semidirect |
| 2. C2×#15689390 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. #20245116 | C2 | semidirect |
| 5. #20245008 | C2 | semidirect |
| 6. #20241500 | C2 | semidirect |
| 7. C2×C47×#509 | C2 | semidirect |
| 203. C2×#509 | D47 | semidirect |
| 240. C47 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253104 | 2 |
| C2×#15689390 | 2 |
| C2×#15688936 | 2 |
| #20245116 | 2 |
| #20245008 | 2 |
| #20241500 | 2 |
| C2×C47×#509 | 2 |
| #13323 | 47 |