Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #20241457 | C2 | semidirect |
| 5. #20241452 | C2 | semidirect |
| 6. #20241451 | C2 | semidirect |
| 7. C47×#1370 | C2 | semidirect |
| 86. C8×C47 | M32 | semidirect |
| 93. C47⋊C8 | M32 | semidirect |
| 111. #1370 | D47 | semidirect |
| 133. C47 | #12017 | semidirect |
| 202. C8 | #13093963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245190 | 2 |
| #20245142 | 2 |
| C8×#10625324 | 2 |
| #20241457 | 2 |
| #20241452 | 2 |
| #20241451 | 2 |
| C47×#1370 | 2 |
| #12017 | 47 |