Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 103 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×#17985776 | C2 | semidirect |
| 4. #22589094 | C2 | semidirect |
| 5. #22586445 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 21. #357×C71 | C4 | semidirect |
| 144. C71 | #13155 | semidirect |
| 156. #357 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985812 | 2 |
| C2×#17985776 | 2 |
| #22589217 | 2 |
| #22589094 | 2 |
| #22586445 | 2 |
| #22586439 | 2 |
| C71×#2140 | 2 |
| #13155 | 71 |