Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×D376 | C2 | semidirect |
| 2. #20245638 | C2 | semidirect |
| 3. #20245424 | C2 | semidirect |
| 4. #20242743 | C2 | semidirect |
| 5. #20241435 | C2 | semidirect |
| 6. #20241350 | C2 | semidirect |
| 7. C47×D4⋊C16 | C2 | semidirect |
| 13. #15689500 | C22 | semidirect |
| 20. #15688876 | C22 | semidirect |
| 23. C47×C4⋊C16 | C22 | semidirect |
| 24. C4×C16×C47 | C22 | semidirect |
| 94. D376 | D8 | semidirect |
| 105. D4×C47 | D16 | semidirect |
| 162. D4⋊C16 | D47 | semidirect |
| 182. C4⋊C16 | C2×D47 | semidirect |
| 184. C4×C16 | C2×D47 | semidirect |
| 187. C47 | #12316 | semidirect |
| 282. D4 | D752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D376 | 2 |
| #20245638 | 2 |
| #20245424 | 2 |
| #20242743 | 2 |
| #20241435 | 2 |
| #20241350 | 2 |
| C47×D4⋊C16 | 2 |
| #12316 | 47 |