Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20245700 | C2 | semidirect |
| 2. C2×#15688958 | C2 | semidirect |
| 3. #20245508 | C2 | semidirect |
| 4. #20241578 | C2 | semidirect |
| 5. #20241572 | C2 | semidirect |
| 6. #20241530 | C2 | semidirect |
| 7. C47×#3415 | C2 | semidirect |
| 8. C2×D752 | C22 | semidirect |
| 13. #15688957 | C22 | semidirect |
| 14. C2×C47⋊C32 | C22 | semidirect |
| 15. #15688953 | C22 | semidirect |
| 116. #3415 | D47 | semidirect |
| 146. C47 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245700 | 2 |
| C2×#15688958 | 2 |
| #20245508 | 2 |
| #20241578 | 2 |
| #20241572 | 2 |
| #20241530 | 2 |
| C47×#3415 | 2 |
| #13669 | 47 |