Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
588 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 588 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. #20251381 | C2 | semidirect |
| 3. #20241214 | C2 | semidirect |
| 4. #20241213 | C2 | semidirect |
| 50. C2×Q8×C47 | SD16 | semidirect |
| 74. C2×Dic94 | SD16 | semidirect |
| 172. C47 | #7749 | semidirect |
| 210. C2×Q8 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251381 | 2 |
| #20244476 | 2 |
| #20241214 | 2 |
| #20241213 | 2 |
| C47×#2014 | 2 |
| #7749 | 47 |