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. #20245466 | C2 | semidirect |
| 3. #20242995 | C2 | semidirect |
| 4. #20241424 | C2 | semidirect |
| 5. #20241361 | C2 | semidirect |
| 6. #20241360 | C2 | semidirect |
| 7. C47×#2214 | C2 | semidirect |
| 17. #15688944 | C22 | semidirect |
| 19. C8×C47⋊C8 | C22 | semidirect |
| 21. C47×#494 | C22 | semidirect |
| 23. C47×#364 | C22 | semidirect |
| 142. #2214 | D47 | semidirect |
| 156. #494 | C2×D47 | semidirect |
| 165. #364 | 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 |
| #20245466 | 2 |
| #20242995 | 2 |
| #20241424 | 2 |
| #20241361 | 2 |
| #20241360 | 2 |
| C47×#2214 | 2 |
| #12312 | 47 |