Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20245293 | C2 | semidirect |
| 4. #20241366 | C2 | semidirect |
| 6. C8×C47⋊C16 | C2 | semidirect |
| 7. C47×#1367 | C2 | semidirect |
| 67. C47⋊C16 | SD16 | semidirect |
| 84. C8×C47 | M32 | semidirect |
| 105. #1367 | D47 | semidirect |
| 128. C47 | #12051 | semidirect |
| 192. C8 | #13093963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245293 | 2 |
| #20245219 | 2 |
| C8×#10625325 | 2 |
| #20241366 | 2 |
| #20241342 | 2 |
| C8×C47⋊C16 | 2 |
| C47×#1367 | 2 |
| #12051 | 47 |