Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 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. #20254766 | C2 | semidirect |
| 2. #20253814 | C2 | semidirect |
| 3. #20242533 | C2 | semidirect |
| 4. #20242504 | C2 | semidirect |
| 5. #20242471 | C2 | semidirect |
| 6. #20242442 | C2 | semidirect |
| 7. #20242123 | C2 | semidirect |
| 8. #20241839 | C2 | semidirect |
| 9. C47×#3549 | C2 | semidirect |
| 11. #15689673 | C22 | semidirect |
| 13. #15689502 | C22 | semidirect |
| 15. #15689497 | C22 | semidirect |
| 17. #15689413 | C22 | semidirect |
| 20. #15689318 | C22 | semidirect |
| 22. #15689147 | C22 | semidirect |
| 23. C2×C4×C47⋊C8 | C22 | semidirect |
| 24. #15688872 | C22 | semidirect |
| 26. D4⋊(C47⋊C8) | C22 | semidirect |
| 27. D4⋊(C47⋊C8) | C22 | semidirect |
| 200. #3549 | D47 | semidirect |
| 242. C47 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254766 | 2 |
| #20253814 | 2 |
| #20242533 | 2 |
| #20242504 | 2 |
| #20242471 | 2 |
| #20242442 | 2 |
| #20242123 | 2 |
| #20241839 | 2 |
| C47×#3549 | 2 |
| #18686 | 47 |