Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20245125 | C2 | semidirect |
| 4. #20245117 | C2 | semidirect |
| 5. #20245105 | C2 | semidirect |
| 6. #20243512 | C2 | semidirect |
| 7. C47×#2110 | C2 | semidirect |
| 13. #15689507 | C4 | semidirect |
| 14. #15689500 | C4 | semidirect |
| 62. M32×C47 | D4 | semidirect |
| 64. C2×C16×C47 | D4 | semidirect |
| 174. #2110 | D47 | semidirect |
| 201. C47 | #13215 | semidirect |
| 233. M32 | D188 | semidirect |
| 235. C2×C16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253874 | 2 |
| C2×#15688937 | 2 |
| #20245125 | 2 |
| #20245117 | 2 |
| #20245105 | 2 |
| #20243512 | 2 |
| C47×#2110 | 2 |
| #13215 | 47 |