Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
202 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 83 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. C4×C71⋊C16 | C4 | semidirect |
| 13. #334×C71 | C4 | semidirect |
| 85. C71 | #7218 | semidirect |
| 95. #334 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590139 | 2 |
| #22588471 | 2 |
| C71×#1568 | 2 |
| #7218 | 71 |