Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 1. #20253788 | C2 | semidirect |
| 2. #20249256 | C2 | semidirect |
| 3. #20242014 | C2 | semidirect |
| 4. #20241935 | C2 | semidirect |
| 5. #20241831 | C2 | semidirect |
| 6. #20241254 | C2 | semidirect |
| 235. C47 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253788 | 2 |
| #20249256 | 2 |
| #20242014 | 2 |
| #20241935 | 2 |
| #20241831 | 2 |
| #20241254 | 2 |
| C47×#3109 | 2 |
| #10019 | 47 |