Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20256522 | C2 | semidirect |
| 2. #20253869 | C2 | semidirect |
| 3. #20245125 | C2 | semidirect |
| 4. #20245104 | C2 | semidirect |
| 5. #20244287 | C2 | semidirect |
| 6. #20241475 | C2 | semidirect |
| 7. C2×C47×#509 | C2 | semidirect |
| 58. C2×C47⋊C16 | D4 | semidirect |
| 71. C2×Q16×C47 | D4 | semidirect |
| 79. C2×D8×C47 | D4 | semidirect |
| 84. M32×C47 | D4 | semidirect |
| 212. C2×#509 | D47 | semidirect |
| 250. C47 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D47 | semidirect |
| 277. C2×D8 | C22⋊D47 | semidirect |
| 295. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #20253869 | 2 |
| #20245125 | 2 |
| #20245104 | 2 |
| #20244287 | 2 |
| #20241475 | 2 |
| C2×C47×#509 | 2 |
| #13334 | 47 |