Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #20256394 | C2 | semidirect |
| 3. #20245616 | C2 | semidirect |
| 4. #20245531 | C2 | semidirect |
| 7. Q8×C16×C47 | C2 | semidirect |
| 72. Q8×C47 | SD32 | semidirect |
| 105. Q8×C16 | D47 | semidirect |
| 127. C47 | #33926 | semidirect |
| 179. Q8 | #13093969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256394 | 2 |
| Q8×D376 | 2 |
| #20245616 | 2 |
| #20245531 | 2 |
| #20245434 | 2 |
| C4×#13093969 | 2 |
| Q8×C16×C47 | 2 |
| #33926 | 47 |