Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C22⋊C16×D47 | C2 | semidirect |
| 3. #340×D47 | C2 | semidirect |
| 4. #20241398 | C2 | semidirect |
| 5. #20241397 | C2 | semidirect |
| 6. #20241396 | C2 | semidirect |
| 7. C47×#1347 | C2 | semidirect |
| 8. C2×D8×D47 | C4 | semidirect |
| 13. #15689360 | C4 | semidirect |
| 17. #15689356 | C4 | semidirect |
| 18. #107×D47 | C4 | semidirect |
| 20. C22⋊(C47⋊C16) | C22 | semidirect |
| 22. #15688886 | C22 | semidirect |
| 25. C47×C22⋊C16 | C22 | semidirect |
| 26. C47×#340 | C22 | semidirect |
| 31. C2×D376 | C2×C4 | semidirect |
| 53. #13093958 | C2×C4 | semidirect |
| 58. C2×D8×C47 | C2×C4 | semidirect |
| 63. #107×C47 | C2×C4 | semidirect |
| 205. #1347 | D47 | direct (N × H) |
| 214. D47 | #1347 | direct (N × H) |
| 230. C22⋊C16 | C2×D47 | semidirect |
| 233. #340 | C2×D47 | semidirect |
| 234. C47 | C2×#1347 | semidirect |
| 242. C2×D8 | C4×D47 | semidirect |
| 268. #107 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D47 | 2 |
| C22⋊C16×D47 | 2 |
| #340×D47 | 2 |
| #20241398 | 2 |
| #20241397 | 2 |
| #20241396 | 2 |
| C47×#1347 | 2 |
| C2×#1347 | 47 |