Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 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×#17985781 | C2 | semidirect |
| 3. #22586327 | C2 | semidirect |
| 4. #22586324 | C2 | semidirect |
| 5. C2×H(3,ℤ/4)×C71 | C2 | semidirect |
| 6. C2×#14556150 | C4 | semidirect |
| 9. #17986257 | C4 | semidirect |
| 11. #17986252 | C4 | semidirect |
| 15. #17986037 | C4 | semidirect |
| 26. C2×Dic284 | C2×C4 | semidirect |
| 28. C2×D568 | C2×C4 | semidirect |
| 42. #14556060 | C2×C4 | semidirect |
| 43. #14556060 | C2×C4 | semidirect |
| 195. C2×H(3,ℤ/4) | D71 | semidirect |
| 198. C71 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597949 | 2 |
| C2×#17985781 | 2 |
| #22586327 | 2 |
| #22586324 | 2 |
| C2×H(3,ℤ/4)×C71 | 2 |
| #11685 | 71 |