Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
382 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 382 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. #22590135 | C2 | semidirect |
| 3. C2×#17985815 | C2 | semidirect |
| 6. #22586451 | C2 | semidirect |
| 7. C2×#362×C71 | C2 | semidirect |
| 162. C2×#362 | D71 | semidirect |
| 166. C71 | #13390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986271 | 2 |
| #22590135 | 2 |
| C2×#17985815 | 2 |
| #22589969 | 2 |
| #22588387 | 2 |
| #22586451 | 2 |
| C2×#362×C71 | 2 |
| #13390 | 71 |