Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1516 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20243385 | C2 | semidirect |
| 3. C2×#15688867 | C2 | semidirect |
| 4. C2×#15688852 | C2 | semidirect |
| 5. C47×#1957 | C2 | semidirect |
| 9. #15689758 | C4 | semidirect |
| 13. C2×C4⋊(C47⋊C8) | C22 | semidirect |
| 20. C2×C4×C8×C47 | C22 | semidirect |
| 21. C47×#384 | C22 | semidirect |
| 158. D188 | #102 | semidirect |
| 193. #1957 | D47 | semidirect |
| 215. C2×C4×C8 | C2×D47 | semidirect |
| 216. #384 | C2×D47 | semidirect |
| 220. C47 | #8443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689758 | 2 |
| #20243385 | 2 |
| C2×#15688867 | 2 |
| C2×#15688852 | 2 |
| C47×#1957 | 2 |
| #8443 | 47 |