Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22588893 | C2 | semidirect |
| 5. #22588628 | C2 | semidirect |
| 6. #22586468 | C2 | semidirect |
| 7. C71×#2129 | C2 | semidirect |
| 196. #2129 | D71 | semidirect |
| 202. C71 | #13433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599207 | 2 |
| #22589989 | 2 |
| #22588893 | 2 |
| #22588865 | 2 |
| #22588628 | 2 |
| #22586468 | 2 |
| C71×#2129 | 2 |
| #13433 | 71 |