Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22586251 | C2 | semidirect |
| 4. #22586250 | C2 | semidirect |
| 5. C71×#1307 | C2 | semidirect |
| 144. #1307 | D71 | semidirect |
| 145. C71 | #8119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596970 | 2 |
| #423×D71 | 2 |
| #22586251 | 2 |
| #22586250 | 2 |
| C71×#1307 | 2 |
| #8119 | 71 |