Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×C16×Dic71 | C2 | semidirect |
| 4. #22589089 | C2 | semidirect |
| 5. #22586435 | C2 | semidirect |
| 6. #22586434 | C2 | semidirect |
| 21. #358×C71 | C4 | semidirect |
| 22. #357×C71 | C4 | semidirect |
| 145. C71 | #13151 | semidirect |
| 157. #358 | Dic71 | semidirect |
| 158. #357 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985806 | 2 |
| C2×C16×Dic71 | 2 |
| #22589229 | 2 |
| #22589089 | 2 |
| #22586435 | 2 |
| #22586434 | 2 |
| C71×#2138 | 2 |
| #13151 | 71 |