Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #20242758 | C2 | semidirect |
| 4. #20241462 | C2 | semidirect |
| 5. #20241438 | C2 | semidirect |
| 7. Q8×C16×C47 | C2 | semidirect |
| 70. C16×C47 | SD16 | semidirect |
| 73. Q8×C47 | SD32 | semidirect |
| 107. Q8×C16 | D47 | semidirect |
| 132. C47 | #12441 | semidirect |
| 180. C16 | #10625336 | semidirect |
| 185. Q8 | #13093969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245644 | 2 |
| #20242758 | 2 |
| #20242748 | 2 |
| #20241462 | 2 |
| #20241438 | 2 |
| #20241435 | 2 |
| Q8×C16×C47 | 2 |
| #12441 | 47 |