Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#15689561 | C2 | semidirect |
| 2. #20252997 | C2 | semidirect |
| 3. C2×#15689376 | C2 | semidirect |
| 4. C2×#15688934 | C2 | semidirect |
| 5. #20245105 | C2 | semidirect |
| 6. #20241494 | C2 | semidirect |
| 7. C2×C47×#349 | C2 | semidirect |
| 38. C2×Dic188 | D4 | semidirect |
| 45. C2×D376 | D4 | semidirect |
| 46. C2×D376 | D4 | semidirect |
| 59. #13093958 | D4 | semidirect |
| 62. #13093956 | D4 | semidirect |
| 78. M32×C47 | D4 | semidirect |
| 219. C2×#349 | D47 | semidirect |
| 251. C47 | #13316 | semidirect |
| 292. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689561 | 2 |
| #20252997 | 2 |
| C2×#15689376 | 2 |
| C2×#15688934 | 2 |
| #20245105 | 2 |
| #20241494 | 2 |
| C2×C47×#349 | 2 |
| #13316 | 47 |