Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 13. Dic71⋊C16 | C4 | semidirect |
| 96. Dic71 | #347 | semidirect |
| 107. C71 | #12658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590095 | 2 |
| C2×#17985776 | 2 |
| #97×Dic71 | 2 |
| #22586420 | 2 |
| C71×#1375 | 2 |
| #12658 | 71 |