Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 15. #366×C71 | C4 | semidirect |
| 56. C16×C71 | C4⋊C4 | semidirect |
| 101. C71 | #13168 | semidirect |
| 109. #366 | Dic71 | semidirect |
| 152. C16 | C4⋊Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985827 | 2 |
| C2×#17985774 | 2 |
| #22589074 | 2 |
| #22586431 | 2 |
| C2×#366×C71 | 2 |
| #13168 | 71 |