Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
366 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 275 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. #20241305 | C2 | direct (N × H) |
| 11. C2×C47⋊C16 | C8 | semidirect |
| 31. C47⋊C16 | C2×C8 | semidirect |
| 53. C2×C47 | #1311 | semidirect |
| 63. C47 | C2×#1311 | semidirect |
| 102. C2 | #20241305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C47⋊C16 | 2 |
| #20241305 | 2 |
| C2×C82×C47 | 2 |
| C2×#1311 | 47 |