Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
314 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 9. C22⋊(C47⋊C16) | C4 | semidirect |
| 12. C22×C16×C47 | C4 | semidirect |
| 55. C22⋊Dic47 | C16 | semidirect |
| 123. C22×C16 | Dic47 | semidirect |
| 132. C47 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C47⋊C16) | 2 |
| C8×C22⋊Dic47 | 2 |
| C2×C47×C22⋊C16 | 2 |
| #7199 | 47 |