Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 3. C2×#15688932 | C2 | semidirect |
| 4. #20245108 | C2 | semidirect |
| 5. C2×#15688905 | C2 | semidirect |
| 6. #20241495 | C2 | semidirect |
| 7. C2×C47×#470 | C2 | semidirect |
| 50. #13093964 | D4 | semidirect |
| 64. C2×Q16×C47 | D4 | semidirect |
| 79. #106×C47 | D4 | semidirect |
| 208. C2×#470 | D47 | semidirect |
| 242. C47 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D47 | semidirect |
| 289. #106 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20252997 | 2 |
| C2×#15688932 | 2 |
| #20245108 | 2 |
| C2×#15688905 | 2 |
| #20241495 | 2 |
| C2×C47×#470 | 2 |
| #13317 | 47 |