Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20252271 | C2 | semidirect |
| 3. #20245125 | C2 | semidirect |
| 4. #20244287 | C2 | semidirect |
| 5. #20241495 | C2 | semidirect |
| 6. #20241473 | C2 | semidirect |
| 7. C2×C47×#360 | C2 | semidirect |
| 10. #15689564 | C4 | semidirect |
| 12. #15689559 | C4 | semidirect |
| 50. #13093964 | C2×C4 | semidirect |
| 65. C2×Q16×C47 | C2×C4 | semidirect |
| 67. C2×D8×C47 | C2×C4 | semidirect |
| 187. C2×#360 | D47 | semidirect |
| 218. C47 | #13030 | semidirect |
| 230. C2×Q16 | C4×D47 | semidirect |
| 234. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #20252271 | 2 |
| #20245125 | 2 |
| #20244287 | 2 |
| #20241495 | 2 |
| #20241473 | 2 |
| C2×C47×#360 | 2 |
| #13030 | 47 |