Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20242913 | C2 | semidirect |
| 4. #20241440 | C2 | semidirect |
| 5. #20241371 | C2 | semidirect |
| 7. C47×#2255 | C2 | semidirect |
| 131. #2255 | D47 | semidirect |
| 160. C47 | #12412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256349 | 2 |
| #20245522 | 2 |
| #20242913 | 2 |
| #20241440 | 2 |
| #20241371 | 2 |
| #20241356 | 2 |
| C47×#2255 | 2 |
| #12412 | 47 |