Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20243103 | C2 | semidirect |
| 4. #20241401 | C2 | semidirect |
| 5. #20241399 | C2 | semidirect |
| 6. #20241397 | C2 | semidirect |
| 7. C47×#1347 | C2 | semidirect |
| 8. C2×#13094043 | C4 | semidirect |
| 13. #15689365 | C4 | semidirect |
| 15. #15689356 | C4 | semidirect |
| 18. #15689160 | C4 | semidirect |
| 191. #1347 | D47 | semidirect |
| 219. C47 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252967 | 2 |
| C22⋊C16×D47 | 2 |
| #20243103 | 2 |
| #20241401 | 2 |
| #20241399 | 2 |
| #20241397 | 2 |
| C47×#1347 | 2 |
| #11703 | 47 |