Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22586431 | C2 | semidirect |
| 4. #22586431 | C2 | semidirect |
| 14. #427×C71 | C4 | semidirect |
| 123. C71 | #12868 | semidirect |
| 128. #427 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C71⋊C16) | 2 |
| #22588369 | 2 |
| #22586431 | 2 |
| C2×#427×C71 | 2 |
| #12868 | 71 |