Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
478 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #20253427 | C2 | semidirect |
| 4. #20242025 | C2 | semidirect |
| 6. #20241251 | C2 | semidirect |
| 7. C47×#1467 | C2 | semidirect |
| 189. #1467 | D47 | semidirect |
| 221. C47 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254401 | 2 |
| #20253510 | 2 |
| #20253427 | 2 |
| #20242025 | 2 |
| #20241856 | 2 |
| #20241251 | 2 |
| C47×#1467 | 2 |
| #10041 | 47 |