Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 109 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×#15689246 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. C2×#15688932 | C2 | semidirect |
| 5. #20241486 | C2 | semidirect |
| 6. #20241468 | C2 | semidirect |
| 7. C47×#1972 | C2 | semidirect |
| 12. C2×#13093968 | C4 | semidirect |
| 13. C2×#13093965 | C4 | semidirect |
| 108. Dic188 | C22⋊C4 | semidirect |
| 110. D376 | C22⋊C4 | semidirect |
| 176. #1972 | D47 | semidirect |
| 204. C47 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689559 | 2 |
| C2×#15689246 | 2 |
| C2×#15688936 | 2 |
| C2×#15688932 | 2 |
| #20241486 | 2 |
| #20241468 | 2 |
| C47×#1972 | 2 |
| #13040 | 47 |