Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
618 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 110. C71 | #21677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591645 | 2 |
| #22589061 | 2 |
| #22588902 | 2 |
| #22588211 | 2 |
| #22588210 | 2 |
| #22588027 | 2 |
| C71×#1832 | 2 |
| #21677 | 71 |