Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
220 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20242286 | C2 | semidirect |
| 3. #20241459 | C2 | semidirect |
| 4. #20241351 | C2 | semidirect |
| 6. #20241305 | C2 | semidirect |
| 67. C47⋊C16 | M16 | semidirect |
| 128. C47 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093968 | 2 |
| #20242286 | 2 |
| #20241459 | 2 |
| #20241351 | 2 |
| #20241349 | 2 |
| #20241305 | 2 |
| C47×#1589 | 2 |
| #12084 | 47 |