Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#17985829 | C2 | semidirect |
| 3. #22590089 | C2 | semidirect |
| 4. C2×#17985782 | C2 | semidirect |
| 5. #22588387 | C2 | semidirect |
| 6. #22586443 | C2 | semidirect |
| 7. C2×#359×C71 | C2 | semidirect |
| 178. C2×#359 | D71 | semidirect |
| 182. C71 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598056 | 2 |
| C2×#17985829 | 2 |
| #22590089 | 2 |
| C2×#17985782 | 2 |
| #22588387 | 2 |
| #22586443 | 2 |
| C2×#359×C71 | 2 |
| #13392 | 71 |