Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20241939 | C2 | semidirect |
| 5. #20241254 | C2 | semidirect |
| 6. #20241252 | C2 | semidirect |
| 7. C47×#1515 | C2 | semidirect |
| 10. #15689471 | C4 | semidirect |
| 11. #15689471 | C4 | semidirect |
| 43. C4×C47⋊C8 | C2×C4 | semidirect |
| 47. C4⋊Q8×C47 | C2×C4 | semidirect |
| 48. C4⋊Q8×C47 | C2×C4 | semidirect |
| 167. #1515 | D47 | semidirect |
| 192. C47 | #9425 | semidirect |
| 198. C4⋊Q8 | C4×D47 | semidirect |
| 199. C4⋊Q8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253764 | 2 |
| #20246564 | 2 |
| #20242101 | 2 |
| #20241939 | 2 |
| #20241254 | 2 |
| #20241252 | 2 |
| C47×#1515 | 2 |
| #9425 | 47 |