Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20245226 | C2 | semidirect |
| 3. #20241463 | C2 | semidirect |
| 4. #20241361 | C2 | semidirect |
| 5. #20241360 | C2 | semidirect |
| 6. C16×C47⋊C8 | C2 | semidirect |
| 7. C47×#2170 | C2 | semidirect |
| 25. #13093970 | C8 | semidirect |
| 26. #13093968 | C8 | semidirect |
| 27. #13093967 | C8 | semidirect |
| 28. #13093965 | C8 | semidirect |
| 101. #2170 | D47 | semidirect |
| 125. C47 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245267 | 2 |
| #20245226 | 2 |
| #20241463 | 2 |
| #20241361 | 2 |
| #20241360 | 2 |
| C16×C47⋊C8 | 2 |
| C47×#2170 | 2 |
| #12046 | 47 |