Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×#13093957 | C2 | semidirect |
| 3. #20242149 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 7. C47×#1285 | C2 | semidirect |
| 9. #15689250 | C4 | semidirect |
| 10. #15689247 | C4 | semidirect |
| 11. #15689200 | C4 | semidirect |
| 13. #15689188 | C4 | semidirect |
| 179. #1285 | D47 | semidirect |
| 209. C47 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252357 | 2 |
| C4×#13093957 | 2 |
| #20242149 | 2 |
| #20241914 | 2 |
| #20241911 | 2 |
| #20241245 | 2 |
| C47×#1285 | 2 |
| #8697 | 47 |