Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20241589 | C2 | semidirect |
| 4. #20241570 | C2 | semidirect |
| 5. #20241568 | C2 | semidirect |
| 7. C47×#1423 | C2 | semidirect |
| 83. #1423 | D47 | semidirect |
| 102. C47 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245480 | 2 |
| #20245169 | 2 |
| #20241589 | 2 |
| #20241570 | 2 |
| #20241568 | 2 |
| (C2×D47)⋊C32 | 2 |
| C47×#1423 | 2 |
| #13716 | 47 |