Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 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. #20245491 | C2 | semidirect |
| 3. #20241575 | C2 | semidirect |
| 4. #20241528 | C2 | semidirect |
| 5. C47×#3414 | C2 | semidirect |
| 6. C2×D752 | C22 | semidirect |
| 10. #15688957 | C22 | semidirect |
| 11. #15688951 | C22 | semidirect |
| 35. Q32×C47 | D4 | semidirect |
| 39. D16×C47 | D4 | semidirect |
| 107. #3414 | D47 | semidirect |
| 130. C47 | #13667 | semidirect |
| 143. Q32 | C22⋊D47 | semidirect |
| 148. D16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245700 | 2 |
| #20245491 | 2 |
| #20241575 | 2 |
| #20241528 | 2 |
| C47×#3414 | 2 |
| #13667 | 47 |