Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
982 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 411 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. C47⋊#1273 | C2 | semidirect |
| 3. C47×#1273 | C2 | semidirect |
| 14. C2×C8×D47 | C8 | semidirect |
| 32. C2×C8×C47 | C2×C8 | semidirect |
| 39. C2×C47⋊C8 | C2×C8 | semidirect |
| 68. #1273 | D47 | direct (N × H) |
| 72. D47 | #1273 | direct (N × H) |
| 79. C47 | C2×#1273 | semidirect |
| 106. C2×C8 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×D47 | 2 |
| C47⋊#1273 | 2 |
| C47×#1273 | 2 |
| C2×#1273 | 47 |