Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22586327 | C2 | direct (N × H) |
| 5. C22×Dic284 | C4 | semidirect |
| 10. #17986257 | C4 | semidirect |
| 12. C2×#14556060 | C4 | semidirect |
| 24. C2×Dic284 | C2×C4 | semidirect |
| 36. #14556060 | C2×C4 | semidirect |
| 165. C2×C71 | #1340 | semidirect |
| 171. C71 | C2×#1340 | semidirect |
| 331. C2 | #22586327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986257 | 2 |
| C2×#17985781 | 2 |
| #22586327 | 2 |
| C2×H(3,ℤ/4)×C71 | 2 |
| C2×#1340 | 71 |