Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. #20243005 | C2 | semidirect |
| 4. #20242997 | C2 | semidirect |
| 5. #20242983 | C2 | semidirect |
| 60. C2×C8×C47 | Q16 | semidirect |
| 136. C47 | #19604 | semidirect |
| 172. C2×C8 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253970 | 2 |
| #20253902 | 2 |
| #20243005 | 2 |
| #20242997 | 2 |
| #20242983 | 2 |
| C2×C8×C47⋊C8 | 2 |
| C47×#3160 | 2 |
| #19604 | 47 |