Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22597470 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586780 | C2 | semidirect |
| 5. C71⋊#1309 | C2 | semidirect |
| 6. #22586230 | C2 | semidirect |
| 7. C71×#1965 | C2 | semidirect |
| 166. Dic142 | #100 | semidirect |
| 205. #1965 | D71 | semidirect |
| 210. C71 | #9360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597816 | 2 |
| #22597470 | 2 |
| #22587008 | 2 |
| #22586780 | 2 |
| C71⋊#1309 | 2 |
| #22586230 | 2 |
| C71×#1965 | 2 |
| #9360 | 71 |