Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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. Q8×C47⋊C16 | C2 | semidirect |
| 4. #20241457 | C2 | semidirect |
| 6. #20241307 | C2 | semidirect |
| 7. C47×Q8⋊C16 | C2 | semidirect |
| 54. #10625336 | C16 | semidirect |
| 70. Q8×C47 | C2×C16 | semidirect |
| 88. C47⋊C8 | C2×C16 | semidirect |
| 106. Q8⋊C16 | D47 | semidirect |
| 128. C47 | SD16⋊C16 | semidirect |
| 176. Q8 | C16×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C47⋊C16 | 2 |
| #20245207 | 2 |
| C8×#10625336 | 2 |
| #20241457 | 2 |
| #20241344 | 2 |
| #20241307 | 2 |
| C47×Q8⋊C16 | 2 |
| SD16⋊C16 | 47 |