Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #20241504 | C2 | semidirect |
| 5. #20241499 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 7. C47×#1833 | C2 | semidirect |
| 127. #1833 | D47 | semidirect |
| 149. C47 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688935 | 2 |
| #20245103 | 2 |
| #20244298 | 2 |
| #20241504 | 2 |
| #20241499 | 2 |
| #20241474 | 2 |
| C47×#1833 | 2 |
| #13490 | 47 |