Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
536 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20254035 | C2 | semidirect |
| 2. #20252286 | C2 | semidirect |
| 3. #20245601 | C2 | semidirect |
| 4. #20245565 | C2 | semidirect |
| 5. #20245564 | C2 | semidirect |
| 6. #20245461 | C2 | semidirect |
| 7. #20245332 | C2 | semidirect |
| 8. #20245289 | C2 | semidirect |
| 9. #20245287 | C2 | semidirect |
| 10. #20245203 | C2 | semidirect |
| 11. C47×#2213 | C2 | semidirect |
| 16. #15689525 | C22 | semidirect |
| 25. #15689235 | C22 | semidirect |
| 30. #15688947 | C22 | semidirect |
| 31. #15688946 | C22 | semidirect |
| 32. #15688944 | C22 | semidirect |
| 33. #15688936 | C22 | semidirect |
| 37. #15688900 | C22 | semidirect |
| 39. C47×#493 | C22 | semidirect |
| 41. C47×#364 | C22 | semidirect |
| 42. C47×#361 | C22 | semidirect |
| 213. #2213 | D47 | semidirect |
| 230. #493 | C2×D47 | semidirect |
| 248. #364 | C2×D47 | semidirect |
| 250. #361 | C2×D47 | semidirect |
| 255. C47 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254035 | 2 |
| #20252286 | 2 |
| #20245601 | 2 |
| #20245565 | 2 |
| #20245564 | 2 |
| #20245461 | 2 |
| #20245332 | 2 |
| #20245289 | 2 |
| #20245287 | 2 |
| #20245203 | 2 |
| C47×#2213 | 2 |
| #33692 | 47 |