Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20245470 | C2 | semidirect |
| 3. #20245469 | C2 | semidirect |
| 4. #20242994 | C2 | semidirect |
| 5. #20241424 | C2 | semidirect |
| 6. #20241362 | C2 | semidirect |
| 7. C47×#1335 | C2 | semidirect |
| 12. #15689503 | C22 | semidirect |
| 19. #15688944 | C22 | semidirect |
| 23. C47×#364 | C22 | semidirect |
| 24. C82×C47 | C22 | semidirect |
| 146. #1335 | D47 | semidirect |
| 165. #364 | C2×D47 | semidirect |
| 168. C82 | C2×D47 | semidirect |
| 169. C47 | #12312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255188 | 2 |
| #20245470 | 2 |
| #20245469 | 2 |
| #20242994 | 2 |
| #20241424 | 2 |
| #20241362 | 2 |
| C47×#1335 | 2 |
| #12312 | 47 |