Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20252485 | C2 | semidirect |
| 3. #20242086 | C2 | semidirect |
| 6. #20241249 | C2 | semidirect |
| 7. C47×#1290 | C2 | semidirect |
| 160. #1290 | D47 | semidirect |
| 188. C47 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254588 | 2 |
| #20252485 | 2 |
| #20242086 | 2 |
| #20242022 | 2 |
| #20241786 | 2 |
| #20241249 | 2 |
| C47×#1290 | 2 |
| #9372 | 47 |