Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
724 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 724 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 |
|---|---|---|
| 2. C2×#15689279 | C2 | semidirect |
| 4. #20241753 | C2 | semidirect |
| 6. #20241275 | C2 | semidirect |
| 7. C47×#1784 | C2 | semidirect |
| 212. #1784 | D47 | semidirect |
| 246. C47 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254195 | 2 |
| C2×#15689279 | 2 |
| C2×#15689262 | 2 |
| #20241753 | 2 |
| #20241749 | 2 |
| #20241275 | 2 |
| C47×#1784 | 2 |
| #9989 | 47 |