Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 24. #13094024 | Q8 | semidirect |
| 25. #13094024 | Q8 | semidirect |
| 176. C47 | #10363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251764 | 2 |
| #20244364 | 2 |
| #20241953 | 2 |
| #20241951 | 2 |
| #20241248 | 2 |
| #20241220 | 2 |
| C47×#1286 | 2 |
| #10363 | 47 |