Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1602 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 395 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. #20243465 | C2 | semidirect |
| 3. #20243462 | C2 | semidirect |
| 4. C2×#15688890 | C2 | semidirect |
| 13. C2×C4×D4×C47 | C4 | semidirect |
| 29. C23×C4×C47 | C2×C4 | semidirect |
| 33. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 37. C2×C22⋊C4×C47 | C2×C4 | semidirect |
| 39. C2×C42×C47 | C2×C4 | semidirect |
| 132. C2×C4×D4 | Dic47 | semidirect |
| 141. C47 | #20689 | semidirect |
| 149. C23×C4 | C2×Dic47 | semidirect |
| 153. C2×C4⋊C4 | C2×Dic47 | semidirect |
| 161. C2×C22⋊C4 | C2×Dic47 | semidirect |
| 163. C2×C42 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245966 | 2 |
| #20243465 | 2 |
| #20243462 | 2 |
| C2×#15688890 | 2 |
| C2×C47×#518 | 2 |
| #20689 | 47 |