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×#15689560 | C2 | semidirect |
| 2. #20253817 | C2 | semidirect |
| 3. #493×D47 | C2 | semidirect |
| 4. #20245653 | C2 | semidirect |
| 5. #20245645 | C2 | semidirect |
| 6. #20245638 | C2 | semidirect |
| 7. #20245637 | C2 | semidirect |
| 8. C4×#13093963 | C2 | semidirect |
| 9. C47×#2248 | C2 | semidirect |
| 17. C2×#13093967 | C22 | semidirect |
| 18. C2×D752 | C22 | semidirect |
| 19. C2×#13093965 | C22 | semidirect |
| 22. #15689508 | C22 | semidirect |
| 24. #15689500 | C22 | semidirect |
| 30. #15688898 | C22 | semidirect |
| 31. C4×C47⋊C16 | C22 | semidirect |
| 32. C2×SD32×C47 | C22 | semidirect |
| 33. C47×#494 | C22 | semidirect |
| 35. C4×C16×C47 | C22 | semidirect |
| 64. #13093963 | D4 | semidirect |
| 120. C16×C47 | C2×D4 | semidirect |
| 121. C47⋊C16 | C2×D4 | semidirect |
| 167. C4×C47 | #509 | semidirect |
| 177. #2248 | D47 | semidirect |
| 195. C2×SD32 | C2×D47 | semidirect |
| 201. #494 | C2×D47 | semidirect |
| 212. C4×C16 | C2×D47 | semidirect |
| 213. C47 | #33717 | semidirect |
| 299. C16 | D4×D47 | semidirect |
| 346. C4 | #15689560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689560 | 2 |
| #20253817 | 2 |
| #493×D47 | 2 |
| #20245653 | 2 |
| #20245645 | 2 |
| #20245638 | 2 |
| #20245637 | 2 |
| C4×#13093963 | 2 |
| C47×#2248 | 2 |
| #33717 | 47 |