Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
510 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#17985777 | C2 | semidirect |
| 4. #22586419 | C2 | semidirect |
| 5. C2×#347×C71 | C2 | semidirect |
| 15. (C2×D71)⋊C16 | C4 | semidirect |
| 37. C2×C71⋊C16 | C2×C4 | semidirect |
| 47. C2×C16×C71 | C2×C4 | semidirect |
| 122. C2×D71 | #347 | semidirect |
| 139. C2×#347 | D71 | semidirect |
| 141. C71 | #12605 | semidirect |
| 179. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D71 | 2 |
| #22589950 | 2 |
| C2×#17985777 | 2 |
| #22586419 | 2 |
| C2×#347×C71 | 2 |
| #12605 | 71 |