Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 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. #20245612 | C2 | semidirect |
| 3. #20245525 | C2 | semidirect |
| 4. #20242778 | C2 | semidirect |
| 5. #20241433 | C2 | semidirect |
| 6. #20241344 | C2 | semidirect |
| 7. C47×#1331 | C2 | semidirect |
| 10. #15689528 | C22 | semidirect |
| 18. C4⋊(C47⋊C16) | C22 | semidirect |
| 23. C4×C16×C47 | C22 | semidirect |
| 24. C47×#335 | C22 | semidirect |
| 70. D8×C47 | SD16 | semidirect |
| 151. #1331 | D47 | semidirect |
| 173. C4×C16 | C2×D47 | semidirect |
| 174. #335 | C2×D47 | semidirect |
| 176. C47 | #12368 | semidirect |
| 227. D8 | #10625325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D188 | 2 |
| #20245612 | 2 |
| #20245525 | 2 |
| #20242778 | 2 |
| #20241433 | 2 |
| #20241344 | 2 |
| C47×#1331 | 2 |
| #12368 | 47 |