Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1426 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 7. C23×Q8×C71 | C4 | semidirect |
| 11. C22×C4⋊C4×C71 | C4 | semidirect |
| 12. C22×C4⋊C4×C71 | C4 | semidirect |
| 18. C2×C22⋊Dic71 | Q8 | semidirect |
| 153. C71 | #11381 | semidirect |
| 154. C23×Q8 | Dic71 | semidirect |
| 158. C22×C4⋊C4 | Dic71 | semidirect |
| 159. C22×C4⋊C4 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985766 | 2 |
| #22586563 | 2 |
| C22×C22⋊Q8×C71 | 2 |
| #11381 | 71 |