Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
284 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 1. #20245670 | C2 | semidirect |
| 3. #20245616 | C2 | semidirect |
| 5. #20242985 | C2 | semidirect |
| 7. C8×C16×C47 | C2 | semidirect |
| 68. C16×C47 | SD16 | semidirect |
| 85. C8×C47 | SD32 | semidirect |
| 106. C8×C16 | D47 | semidirect |
| 126. C47 | #12505 | semidirect |
| 172. C16 | #10625325 | semidirect |
| 189. C8 | #13093969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245670 | 2 |
| #20245644 | 2 |
| #20245616 | 2 |
| #20245612 | 2 |
| #20242985 | 2 |
| #20242980 | 2 |
| C8×C16×C47 | 2 |
| #12505 | 47 |