Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
232 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 2. Q8×C47⋊C16 | C2 | semidirect |
| 4. #20241461 | C2 | semidirect |
| 5. #20241437 | C2 | semidirect |
| 7. C47×#1670 | C2 | semidirect |
| 70. C47⋊C16 | SD16 | semidirect |
| 75. Q8×C47 | SD32 | semidirect |
| 108. #1670 | D47 | semidirect |
| 132. C47 | #12441 | semidirect |
| 185. Q8 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245645 | 2 |
| Q8×C47⋊C16 | 2 |
| #20242748 | 2 |
| #20241461 | 2 |
| #20241437 | 2 |
| #20241433 | 2 |
| C47×#1670 | 2 |
| #12441 | 47 |