Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 8. C71⋊#338 | C4 | semidirect |
| 11. C2×M32×C71 | C4 | semidirect |
| 12. C22×C16×C71 | C4 | semidirect |
| 114. C71 | #7227 | semidirect |
| 116. C2×M32 | Dic71 | semidirect |
| 117. C22×C16 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588390 | 2 |
| #22588386 | 2 |
| C71×#2113 | 2 |
| #7227 | 71 |