Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20251341 | C2 | semidirect |
| 5. #20241213 | C2 | semidirect |
| 6. #20241212 | C2 | semidirect |
| 7. C47×#1271 | C2 | semidirect |
| 105. C4⋊C4×C47 | SD16 | semidirect |
| 208. #1271 | D47 | semidirect |
| 236. C47 | #7747 | semidirect |
| 327. C4⋊C4 | #10625325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251341 | 2 |
| #20244623 | 2 |
| #20244622 | 2 |
| #20244478 | 2 |
| #20241213 | 2 |
| #20241212 | 2 |
| C47×#1271 | 2 |
| #7747 | 47 |