Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 1. #20254998 | C2 | semidirect |
| 2. #20245652 | C2 | semidirect |
| 3. #20242864 | C2 | semidirect |
| 4. #20241432 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241345 | C2 | semidirect |
| 7. C47×#2206 | C2 | semidirect |
| 19. #15688899 | C22 | semidirect |
| 20. #15688874 | C22 | semidirect |
| 23. C47×#493 | C22 | semidirect |
| 25. C47×C4⋊C16 | C22 | semidirect |
| 88. D8×C47 | D8 | semidirect |
| 175. #2206 | D47 | semidirect |
| 193. #493 | C2×D47 | semidirect |
| 201. C4⋊C16 | C2×D47 | semidirect |
| 206. C47 | #12324 | semidirect |
| 275. D8 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254998 | 2 |
| #20245652 | 2 |
| #20242864 | 2 |
| #20241432 | 2 |
| #20241355 | 2 |
| #20241345 | 2 |
| C47×#2206 | 2 |
| #12324 | 47 |