Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
374 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245641 | C2 | semidirect |
| 3. #20245434 | C2 | semidirect |
| 4. #20242753 | C2 | semidirect |
| 5. #20241438 | C2 | semidirect |
| 6. #20241350 | C2 | semidirect |
| 7. C47×D4⋊C16 | C2 | semidirect |
| 145. D4⋊C16 | D47 | semidirect |
| 168. C47 | #12323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255110 | 2 |
| #20245641 | 2 |
| #20245434 | 2 |
| #20242753 | 2 |
| #20241438 | 2 |
| #20241350 | 2 |
| C47×D4⋊C16 | 2 |
| #12323 | 47 |