Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17985824 | C2 | semidirect |
| 3. C2×#17985806 | C2 | semidirect |
| 4. C2×#17985784 | C2 | semidirect |
| 5. #22588405 | C2 | semidirect |
| 6. #22586449 | C2 | semidirect |
| 7. C71×#2139 | C2 | semidirect |
| 44. C2×C71⋊C16 | D4 | semidirect |
| 187. #2139 | D71 | semidirect |
| 191. C71 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598006 | 2 |
| C2×#17985824 | 2 |
| C2×#17985806 | 2 |
| C2×#17985784 | 2 |
| #22588405 | 2 |
| #22586449 | 2 |
| C71×#2139 | 2 |
| #13384 | 71 |