Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20252427 | C2 | semidirect |
| 3. #20243308 | C2 | semidirect |
| 4. #20243308 | C2 | semidirect |
| 5. #20241724 | C2 | semidirect |
| 6. #20241294 | C2 | semidirect |
| 7. C47×#1305 | C2 | semidirect |
| 41. C2×#10625329 | D4 | semidirect |
| 67. C2×M16×C47 | D4 | semidirect |
| 190. C2×Dic47 | #100 | semidirect |
| 246. #1305 | D47 | semidirect |
| 277. C47 | #9504 | semidirect |
| 294. C2×M16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252427 | 2 |
| #20246745 | 2 |
| #20243308 | 2 |
| #20241724 | 2 |
| #20241294 | 2 |
| C47×#1305 | 2 |
| #9504 | 47 |