Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20245137 | C2 | semidirect |
| 2. C2×#15688936 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. #20245116 | C2 | semidirect |
| 5. #20244178 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 38. #13093960 | D4 | semidirect |
| 201. C47 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245137 | 2 |
| C2×#15688936 | 2 |
| #20245116 | 2 |
| #20244178 | 2 |
| #20241474 | 2 |
| C47×#3155 | 2 |
| #13417 | 47 |