Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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. C8×D376 | C2 | semidirect |
| 3. #20241461 | C2 | semidirect |
| 4. #20241349 | C2 | semidirect |
| 5. #20241348 | C2 | semidirect |
| 6. #20241305 | C2 | semidirect |
| 7. C8×D8×C47 | C2 | semidirect |
| 26. #13093965 | C8 | semidirect |
| 49. D8×C47 | C2×C8 | semidirect |
| 64. D376 | C2×C8 | semidirect |
| 68. C47⋊C16 | C2×C8 | semidirect |
| 109. C8×D8 | D47 | semidirect |
| 134. C47 | #12045 | semidirect |
| 163. D8 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093965 | 2 |
| C8×D376 | 2 |
| #20241461 | 2 |
| #20241349 | 2 |
| #20241348 | 2 |
| #20241305 | 2 |
| C8×D8×C47 | 2 |
| #12045 | 47 |