Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245532 | C2 | semidirect |
| 3. #20242784 | C2 | semidirect |
| 4. #20241434 | C2 | semidirect |
| 5. #20241350 | C2 | semidirect |
| 6. #20241344 | C2 | semidirect |
| 7. C47×#2240 | C2 | semidirect |
| 17. C4⋊(C47⋊C16) | C22 | semidirect |
| 19. #15688876 | C22 | semidirect |
| 21. C47×#500 | C22 | semidirect |
| 24. C4×C16×C47 | C22 | semidirect |
| 145. #2240 | D47 | semidirect |
| 159. #500 | C2×D47 | semidirect |
| 171. C4×C16 | C2×D47 | semidirect |
| 174. C47 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255063 | 2 |
| #20245532 | 2 |
| #20242784 | 2 |
| #20241434 | 2 |
| #20241350 | 2 |
| #20241344 | 2 |
| C47×#2240 | 2 |
| #12372 | 47 |