Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20256538 | C2 | semidirect |
| 2. #20256537 | C2 | semidirect |
| 3. #20245708 | C2 | semidirect |
| 4. #20245707 | C2 | semidirect |
| 5. #20245704 | C2 | semidirect |
| 6. #20245696 | C2 | semidirect |
| 7. #20245695 | C2 | semidirect |
| 8. C2×#15688963 | C2 | semidirect |
| 9. Q64×D47 | C2 | semidirect |
| 10. #20245683 | C2 | semidirect |
| 11. C47×#2264 | C2 | semidirect |
| 160. #2264 | D47 | semidirect |
| 200. C47 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256538 | 2 |
| #20256537 | 2 |
| #20245708 | 2 |
| #20245707 | 2 |
| #20245704 | 2 |
| #20245696 | 2 |
| #20245695 | 2 |
| C2×#15688963 | 2 |
| Q64×D47 | 2 |
| #20245683 | 2 |
| C47×#2264 | 2 |
| #33984 | 47 |