Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 2. #20245615 | C2 | semidirect |
| 4. #20241442 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 7. C47×#2209 | C2 | semidirect |
| 126. #2209 | D47 | semidirect |
| 152. C47 | #12345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255820 | 2 |
| #20245615 | 2 |
| #20242750 | 2 |
| #20241442 | 2 |
| #20241352 | 2 |
| #20241342 | 2 |
| C47×#2209 | 2 |
| #12345 | 47 |