Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22590587 | C2 | semidirect |
| 4. #22590586 | C2 | semidirect |
| 5. #22590585 | C2 | semidirect |
| 6. #22590584 | C2 | semidirect |
| 9. C71×#2245 | C2 | semidirect |
| 145. D71 | #2245 | direct (N × H) |
| 152. #2245 | D71 | direct (N × H) |
| 155. C71 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D71 | 2 |
| #494×D71 | 2 |
| #22590587 | 2 |
| #22590586 | 2 |
| #22590585 | 2 |
| #22590584 | 2 |
| #358×D71 | 2 |
| #346×D71 | 2 |
| C71×#2245 | 2 |
| C2×#2245 | 71 |