Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#15689556 | C2 | semidirect |
| 2. #20255147 | C2 | semidirect |
| 3. #20245638 | C2 | semidirect |
| 4. #20245475 | C2 | semidirect |
| 5. #20245428 | C2 | semidirect |
| 6. #20245314 | C2 | semidirect |
| 7. C16×D188 | C2 | semidirect |
| 8. C4×Q32×C47 | C2 | semidirect |
| 52. Q32×C47 | D4 | semidirect |
| 125. C4×C47 | #508 | semidirect |
| 135. C4×Q32 | D47 | semidirect |
| 162. C47 | #33853 | semidirect |
| 178. Q32 | D188 | semidirect |
| 259. C4 | #15689556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689556 | 2 |
| #20255147 | 2 |
| #20245638 | 2 |
| #20245475 | 2 |
| #20245428 | 2 |
| #20245314 | 2 |
| C16×D188 | 2 |
| C4×Q32×C47 | 2 |
| #33853 | 47 |