Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20245170 | C2 | semidirect |
| 5. #20241490 | C2 | semidirect |
| 6. #20241485 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 135. #1389 | D47 | semidirect |
| 158. C47 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245170 | 2 |
| C2×#15688908 | 2 |
| #20243443 | 2 |
| #20243431 | 2 |
| #20241490 | 2 |
| #20241485 | 2 |
| C47×#1389 | 2 |
| #13500 | 47 |