Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 2. #20245143 | C2 | semidirect |
| 3. C2×#15688937 | C2 | semidirect |
| 4. C2×#15688936 | C2 | semidirect |
| 5. C2×#15688935 | C2 | semidirect |
| 6. #108×Dic47 | C2 | semidirect |
| 7. C2×C47×#361 | C2 | semidirect |
| 47. #13093960 | D4 | semidirect |
| 65. #108×C47 | D4 | semidirect |
| 167. Dic47 | #361 | semidirect |
| 173. C2×#361 | D47 | semidirect |
| 199. C47 | #13257 | semidirect |
| 235. #108 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689498 | 2 |
| #20245143 | 2 |
| C2×#15688937 | 2 |
| C2×#15688936 | 2 |
| C2×#15688935 | 2 |
| #108×Dic47 | 2 |
| C2×C47×#361 | 2 |
| #13257 | 47 |