Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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×C22⋊(C71⋊C16) | C2 | semidirect |
| 3. #22586351 | C2 | semidirect |
| 4. #22586348 | C2 | semidirect |
| 5. C71×#1807 | C2 | semidirect |
| 6. C2×#14556150 | C4 | semidirect |
| 9. #17986240 | C4 | semidirect |
| 11. #17986235 | C4 | semidirect |
| 15. #17986037 | C4 | semidirect |
| 174. #1807 | D71 | semidirect |
| 177. C71 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| C2×C22⋊(C71⋊C16) | 2 |
| #22586351 | 2 |
| #22586348 | 2 |
| C71×#1807 | 2 |
| #11885 | 71 |