Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20241462 | C2 | semidirect |
| 5. #20241443 | C2 | semidirect |
| 6. #20241437 | C2 | semidirect |
| 7. C47×#2241 | C2 | semidirect |
| 103. #2241 | D47 | semidirect |
| 129. C47 | #12470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D188 | 2 |
| #20242774 | 2 |
| #20242750 | 2 |
| #20241462 | 2 |
| #20241443 | 2 |
| #20241437 | 2 |
| C47×#2241 | 2 |
| #12470 | 47 |