Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22588504 | C2 | semidirect |
| 4. #22586432 | C2 | semidirect |
| 5. C71×#1374 | C2 | semidirect |
| 120. #1374 | D71 | semidirect |
| 121. C71 | #13482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985801 | 2 |
| #22589206 | 2 |
| #22588504 | 2 |
| #22586432 | 2 |
| C71×#1374 | 2 |
| #13482 | 71 |