Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20256490 | C2 | semidirect |
| 3. #20245105 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. #20243431 | C2 | semidirect |
| 6. #20241489 | C2 | semidirect |
| 7. C47×#1384 | C2 | semidirect |
| 15. #15689377 | C4 | semidirect |
| 49. C2×C47⋊C16 | D4 | semidirect |
| 60. C2×C16×C47 | D4 | semidirect |
| 170. #1384 | D47 | semidirect |
| 195. C47 | #13074 | semidirect |
| 226. C2×C16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256490 | 2 |
| #20253037 | 2 |
| #20245105 | 2 |
| #20245103 | 2 |
| #20243431 | 2 |
| #20241489 | 2 |
| C47×#1384 | 2 |
| #13074 | 47 |