Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C2×#17985833 | C2 | semidirect |
| 2. C2×#17985825 | C2 | semidirect |
| 3. #22586521 | C2 | semidirect |
| 4. #22586518 | C2 | semidirect |
| 13. #508×C71 | C4 | semidirect |
| 30. Q32×C71 | C2×C4 | semidirect |
| 33. D16×C71 | C2×C4 | semidirect |
| 101. C71 | #13616 | semidirect |
| 104. #508 | Dic71 | semidirect |
| 123. Q32 | C2×Dic71 | semidirect |
| 126. D16 | C2×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985833 | 2 |
| C2×#17985825 | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C2×#508×C71 | 2 |
| #13616 | 71 |