Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 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. #20254303 | C2 | semidirect |
| 2. #20253841 | C2 | semidirect |
| 3. #20242471 | C2 | semidirect |
| 4. #20242442 | C2 | semidirect |
| 5. #20242050 | C2 | semidirect |
| 6. #20241805 | C2 | semidirect |
| 7. C47×#3549 | C2 | semidirect |
| 9. C2×#13094021 | C22 | semidirect |
| 13. #15689497 | C22 | semidirect |
| 15. #15689318 | C22 | semidirect |
| 17. #15689176 | C22 | semidirect |
| 18. C4×#10625329 | C22 | semidirect |
| 19. #15688872 | C22 | semidirect |
| 20. #15688867 | C22 | semidirect |
| 21. D4⋊(C47⋊C8) | C22 | semidirect |
| 24. C47×#555 | C22 | semidirect |
| 26. D42×C47 | C22 | semidirect |
| 174. #3549 | D47 | semidirect |
| 190. #555 | C2×D47 | semidirect |
| 192. D42 | C2×D47 | semidirect |
| 210. C47 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254303 | 2 |
| #20253841 | 2 |
| #20242471 | 2 |
| #20242442 | 2 |
| #20242050 | 2 |
| #20241805 | 2 |
| C47×#3549 | 2 |
| #18714 | 47 |