Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 1. C2×#15689564 | C2 | semidirect |
| 2. C22×#13093967 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. C2×#15688929 | C2 | semidirect |
| 6. #20241477 | C2 | semidirect |
| 7. C47×#1979 | C2 | semidirect |
| 58. #13093964 | D4 | semidirect |
| 62. C2×C47⋊C16 | D4 | semidirect |
| 69. C2×Q16×C47 | D4 | semidirect |
| 201. #1979 | D47 | semidirect |
| 232. C47 | #13338 | semidirect |
| 248. C2×Q16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| C22×#13093967 | 2 |
| #20253874 | 2 |
| C2×#15688935 | 2 |
| C2×#15688929 | 2 |
| #20241477 | 2 |
| C47×#1979 | 2 |
| #13338 | 47 |