Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#15688947 | C2 | semidirect |
| 5. #20241487 | C2 | semidirect |
| 6. #20241486 | C2 | semidirect |
| 7. C2×C47×#365 | C2 | semidirect |
| 18. (C2×D47)⋊C16 | C4 | semidirect |
| 40. C2×C47⋊C16 | C2×C4 | semidirect |
| 52. C2×C16×C47 | C2×C4 | semidirect |
| 135. C2×D47 | #365 | semidirect |
| 145. C2×#365 | D47 | semidirect |
| 171. C47 | #12929 | semidirect |
| 194. C2×C16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×D47 | 2 |
| C2×#15688947 | 2 |
| #20244998 | 2 |
| #20243423 | 2 |
| #20241487 | 2 |
| #20241486 | 2 |
| C2×C47×#365 | 2 |
| #12929 | 47 |