Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
912 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20254326 | C2 | semidirect |
| 3. #20242057 | C2 | semidirect |
| 4. #20241221 | C2 | semidirect |
| 5. C47×#1994 | C2 | semidirect |
| 31. C4⋊(C47⋊C8) | D4 | semidirect |
| 36. C4⋊Q8×C47 | D4 | semidirect |
| 71. C42×C47 | SD16 | semidirect |
| 120. #1994 | D47 | semidirect |
| 140. C47 | #10290 | semidirect |
| 147. C4⋊Q8 | D188 | semidirect |
| 195. C42 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254326 | 2 |
| #20251783 | 2 |
| #20242057 | 2 |
| #20241221 | 2 |
| C47×#1994 | 2 |
| #10290 | 47 |