Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17986122 | C2 | semidirect |
| 3. #22590087 | C2 | semidirect |
| 4. #22590068 | C2 | semidirect |
| 5. #22586453 | C2 | semidirect |
| 6. #22586424 | C2 | semidirect |
| 7. C71×#1975 | C2 | semidirect |
| 10. #17986440 | C4 | semidirect |
| 12. #17986435 | C4 | semidirect |
| 186. #1975 | D71 | semidirect |
| 189. C71 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| C2×#17986122 | 2 |
| #22590087 | 2 |
| #22590068 | 2 |
| #22586453 | 2 |
| #22586424 | 2 |
| C71×#1975 | 2 |
| #13024 | 71 |