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. #20254124 | C2 | semidirect |
| 2. #20252293 | C2 | semidirect |
| 3. #20245601 | C2 | semidirect |
| 4. #20245560 | C2 | semidirect |
| 5. #20245559 | C2 | semidirect |
| 6. #20245461 | C2 | semidirect |
| 7. #20245332 | C2 | semidirect |
| 8. #20245289 | C2 | semidirect |
| 9. #20245287 | C2 | semidirect |
| 10. #20245199 | C2 | semidirect |
| 11. C47×#2213 | C2 | semidirect |
| 16. #15689521 | C22 | semidirect |
| 26. #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 |
| 113. Q16×C47 | #41 | semidirect |
| 119. D8×C47 | #41 | semidirect |
| 141. Dic188 | #41 | semidirect |
| 142. D376 | #41 | semidirect |
| 221. #2213 | D47 | semidirect |
| 238. #493 | C2×D47 | semidirect |
| 256. #364 | C2×D47 | semidirect |
| 258. #361 | C2×D47 | semidirect |
| 263. C47 | #33688 | semidirect |
| 336. Q16 | #10625352 | semidirect |
| 347. D8 | #10625352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254124 | 2 |
| #20252293 | 2 |
| #20245601 | 2 |
| #20245560 | 2 |
| #20245559 | 2 |
| #20245461 | 2 |
| #20245332 | 2 |
| #20245289 | 2 |
| #20245287 | 2 |
| #20245199 | 2 |
| C47×#2213 | 2 |
| #33688 | 47 |