Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 3. C4×#13093955 | C2 | semidirect |
| 4. #20243218 | C2 | semidirect |
| 6. #20243075 | C2 | semidirect |
| 7. C47×#2276 | C2 | semidirect |
| 10. C4×#10625336 | C4 | semidirect |
| 35. #13093955 | C2×C4 | semidirect |
| 36. #13093948 | C2×C4 | semidirect |
| 39. C4×C47⋊C8 | C2×C4 | semidirect |
| 43. C4×Q8×C47 | C2×C4 | semidirect |
| 72. #10625336 | C42 | semidirect |
| 119. #2276 | D47 | semidirect |
| 146. C47 | #20506 | semidirect |
| 154. C4×Q8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#10625336 | 2 |
| #20245750 | 2 |
| C4×#13093955 | 2 |
| #20243218 | 2 |
| #20243216 | 2 |
| #20243075 | 2 |
| C47×#2276 | 2 |
| #20506 | 47 |