Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#17985776 | C2 | semidirect |
| 5. #22589094 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 16. #17985799 | C4 | semidirect |
| 142. #1386 | D71 | semidirect |
| 144. C71 | #13155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985813 | 2 |
| #22590055 | 2 |
| C2×#17985776 | 2 |
| #22589214 | 2 |
| #22589094 | 2 |
| #22586438 | 2 |
| C71×#1386 | 2 |
| #13155 | 71 |