Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20254126 | C2 | semidirect |
| 2. #20245602 | C2 | semidirect |
| 3. #20245559 | C2 | semidirect |
| 4. #20245464 | C2 | semidirect |
| 5. #20245334 | C2 | semidirect |
| 6. #20245286 | C2 | semidirect |
| 7. #20245200 | C2 | semidirect |
| 8. C47×#2956 | C2 | semidirect |
| 11. #15689521 | C22 | semidirect |
| 12. #15689500 | C22 | semidirect |
| 17. #15689236 | C22 | semidirect |
| 18. #15688947 | C22 | semidirect |
| 19. #15688944 | C22 | semidirect |
| 20. #15688935 | C22 | semidirect |
| 23. #15688901 | C22 | semidirect |
| 89. Q16×C47 | #41 | semidirect |
| 93. D8×C47 | #41 | semidirect |
| 166. #2956 | D47 | semidirect |
| 202. C47 | #33688 | semidirect |
| 259. Q16 | #10625350 | semidirect |
| 265. D8 | #10625350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254126 | 2 |
| #20245602 | 2 |
| #20245559 | 2 |
| #20245464 | 2 |
| #20245334 | 2 |
| #20245286 | 2 |
| #20245200 | 2 |
| C47×#2956 | 2 |
| #33688 | 47 |