Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
440 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 30. #14556039 | Q8 | semidirect |
| 140. C71 | #9895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596718 | 2 |
| #22588089 | 2 |
| #22586222 | 2 |
| C71×#1767 | 2 |
| #9895 | 71 |