Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #20242985 | C2 | semidirect |
| 5. #20241445 | C2 | semidirect |
| 6. #20241438 | C2 | semidirect |
| 7. C47×#1367 | C2 | semidirect |
| 87. C8×C47 | SD32 | semidirect |
| 108. #1367 | D47 | semidirect |
| 130. C47 | #12420 | semidirect |
| 196. C8 | #13093969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245536 | 2 |
| #20245434 | 2 |
| #20242985 | 2 |
| C8×D376 | 2 |
| #20241445 | 2 |
| #20241438 | 2 |
| C47×#1367 | 2 |
| #12420 | 47 |