Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586453 | C2 | semidirect |
| 4. #22586420 | C2 | semidirect |
| 5. C71×#1849 | C2 | semidirect |
| 112. #1849 | D71 | semidirect |
| 115. C71 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590087 | 2 |
| #22589233 | 2 |
| #22586453 | 2 |
| #22586420 | 2 |
| C71×#1849 | 2 |
| #13486 | 71 |