Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590009 | C2 | semidirect |
| 3. #22586516 | C2 | semidirect |
| 4. #22586498 | C2 | semidirect |
| 5. C71×#2134 | C2 | semidirect |
| 6. #17986604 | C4 | semidirect |
| 8. #17986375 | C4 | semidirect |
| 9. #17986363 | C4 | semidirect |
| 15. #17986060 | C4 | semidirect |
| 27. #14556125 | C2×C4 | semidirect |
| 28. #14556120 | C2×C4 | semidirect |
| 42. #14556039 | C2×C4 | semidirect |
| 43. C4×C71⋊C8 | C2×C4 | semidirect |
| 160. #2134 | D71 | semidirect |
| 164. C71 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599390 | 2 |
| #22590009 | 2 |
| #22586516 | 2 |
| #22586498 | 2 |
| C71×#2134 | 2 |
| #13605 | 71 |