Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #20241461 | C2 | semidirect |
| 4. #20241352 | C2 | semidirect |
| 6. C8×C47⋊C16 | C2 | semidirect |
| 7. C8×Q16×C47 | C2 | semidirect |
| 26. #13093967 | C8 | direct (N × H) |
| 48. Q16×C47 | C2×C8 | semidirect |
| 67. C47⋊C16 | C2×C8 | semidirect |
| 85. C8×C47 | SD32 | semidirect |
| 103. C8×Q16 | D47 | semidirect |
| 128. C47 | C8×SD32 | semidirect |
| 154. Q16 | C8×D47 | semidirect |
| 192. C8 | #13093967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093967 | 2 |
| C8×D376 | 2 |
| #20241461 | 2 |
| #20241352 | 2 |
| #20241348 | 2 |
| C8×C47⋊C16 | 2 |
| C8×Q16×C47 | 2 |
| C8×SD32 | 47 |