Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q16×Dic94 | C2 | semidirect |
| 4. #20241445 | C2 | semidirect |
| 5. #20241366 | C2 | semidirect |
| 6. #20241352 | C2 | semidirect |
| 61. Q16×C47 | SD16 | semidirect |
| 103. Dic94 | SD32 | semidirect |
| 152. C47 | #12354 | semidirect |
| 189. Q16 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic94 | 2 |
| #20245611 | 2 |
| #20242745 | 2 |
| #20241445 | 2 |
| #20241366 | 2 |
| #20241352 | 2 |
| C47×#2207 | 2 |
| #12354 | 47 |