Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#15689557 | C2 | semidirect |
| 2. #20253815 | C2 | semidirect |
| 3. #493×D47 | C2 | semidirect |
| 4. #20245651 | C2 | semidirect |
| 5. #20245644 | C2 | semidirect |
| 6. #20245643 | C2 | semidirect |
| 7. #20245637 | C2 | semidirect |
| 8. C4×#13093963 | C2 | semidirect |
| 9. C47×#2246 | C2 | semidirect |
| 17. C2×#13093969 | C22 | semidirect |
| 18. C2×#13093968 | C22 | semidirect |
| 19. C2×#13093965 | C22 | semidirect |
| 22. #15689506 | C22 | semidirect |
| 23. #15689503 | C22 | semidirect |
| 30. #15688898 | C22 | semidirect |
| 31. C4×C47⋊C16 | C22 | semidirect |
| 32. C2×D16×C47 | C22 | semidirect |
| 34. C47×#493 | C22 | semidirect |
| 35. C4×C16×C47 | C22 | semidirect |
| 64. #13093963 | D4 | semidirect |
| 120. C16×C47 | C2×D4 | semidirect |
| 121. C47⋊C16 | C2×D4 | semidirect |
| 166. C4×C47 | #509 | semidirect |
| 179. #2246 | D47 | semidirect |
| 197. C2×D16 | C2×D47 | semidirect |
| 207. #493 | C2×D47 | semidirect |
| 212. C4×C16 | C2×D47 | semidirect |
| 213. C47 | #33717 | semidirect |
| 299. C16 | D4×D47 | semidirect |
| 346. C4 | #15689557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689557 | 2 |
| #20253815 | 2 |
| #493×D47 | 2 |
| #20245651 | 2 |
| #20245644 | 2 |
| #20245643 | 2 |
| #20245637 | 2 |
| C4×#13093963 | 2 |
| C47×#2246 | 2 |
| #33717 | 47 |