Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #20242194 | C2 | semidirect |
| 4. #20241351 | C2 | semidirect |
| 6. #20241304 | C2 | semidirect |
| 7. C47×#1371 | C2 | semidirect |
| 28. #13093969 | C8 | semidirect |
| 61. Dic188 | C2×C8 | semidirect |
| 66. C16×C47 | C2×C8 | semidirect |
| 105. #1371 | D47 | semidirect |
| 128. C47 | #12043 | semidirect |
| 173. C16 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093969 | 2 |
| #20242194 | 2 |
| #20242182 | 2 |
| #20241351 | 2 |
| #20241348 | 2 |
| #20241304 | 2 |
| C47×#1371 | 2 |
| #12043 | 47 |