Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #20241446 | C2 | semidirect |
| 5. Q8⋊(C47⋊C16) | C2 | semidirect |
| 6. #20241352 | C2 | semidirect |
| 7. Q8×Q16×C47 | C2 | semidirect |
| 61. Q16×C47 | SD16 | semidirect |
| 90. Q8×C47 | SD32 | semidirect |
| 124. Q8×Q16 | D47 | semidirect |
| 152. C47 | #12354 | semidirect |
| 189. Q16 | #10625336 | semidirect |
| 218. Q8 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245613 | 2 |
| #20245428 | 2 |
| #20242748 | 2 |
| #20241446 | 2 |
| Q8⋊(C47⋊C16) | 2 |
| #20241352 | 2 |
| Q8×Q16×C47 | 2 |
| #12354 | 47 |