Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 88. C71⋊C8 | #108 | semidirect |
| 112. C71 | #8828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588478 | 2 |
| #22587098 | 2 |
| #22587095 | 2 |
| C2×#17985721 | 2 |
| C71×#1848 | 2 |
| #8828 | 71 |