Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20243512 | C2 | semidirect |
| 5. #20241494 | C2 | semidirect |
| 6. #20241487 | C2 | semidirect |
| 7. C47×#2153 | C2 | semidirect |
| 10. #15689236 | C4 | semidirect |
| 11. #15689231 | C4 | semidirect |
| 147. #2153 | D47 | semidirect |
| 175. C47 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252273 | 2 |
| #20245125 | 2 |
| #20245117 | 2 |
| #20243512 | 2 |
| #20241494 | 2 |
| #20241487 | 2 |
| C47×#2153 | 2 |
| #12828 | 47 |