Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 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. #20254127 | C2 | semidirect |
| 2. #20252293 | C2 | semidirect |
| 3. #20245604 | C2 | semidirect |
| 4. #20245556 | C2 | semidirect |
| 5. #20245465 | C2 | semidirect |
| 6. #20245464 | C2 | semidirect |
| 7. #20245335 | C2 | semidirect |
| 8. #20245285 | C2 | semidirect |
| 9. #20245283 | C2 | semidirect |
| 10. #20245199 | C2 | semidirect |
| 11. C47×#2230 | C2 | semidirect |
| 17. #15689500 | C22 | semidirect |
| 27. #15689234 | C22 | semidirect |
| 31. #15688945 | C22 | semidirect |
| 32. #15688944 | C22 | semidirect |
| 33. #15688937 | C22 | semidirect |
| 34. #15688935 | C22 | semidirect |
| 37. #15688900 | C22 | semidirect |
| 38. C47×#498 | C22 | semidirect |
| 40. C47×#365 | C22 | semidirect |
| 41. C47×#364 | C22 | semidirect |
| 113. Q16×C47 | #41 | semidirect |
| 115. D8×C47 | #41 | semidirect |
| 137. Dic188 | #41 | semidirect |
| 142. D376 | #41 | semidirect |
| 219. #2230 | D47 | semidirect |
| 237. #498 | C2×D47 | semidirect |
| 254. #365 | C2×D47 | semidirect |
| 256. #364 | C2×D47 | semidirect |
| 263. C47 | #33688 | semidirect |
| 336. Q16 | #10625354 | semidirect |
| 347. D8 | #10625354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254127 | 2 |
| #20252293 | 2 |
| #20245604 | 2 |
| #20245556 | 2 |
| #20245465 | 2 |
| #20245464 | 2 |
| #20245335 | 2 |
| #20245285 | 2 |
| #20245283 | 2 |
| #20245199 | 2 |
| C47×#2230 | 2 |
| #33688 | 47 |