Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17985823 | C2 | semidirect |
| 5. #22586439 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C2×#365×C71 | C2 | semidirect |
| 18. (C2×D71)⋊C16 | C4 | semidirect |
| 147. C2×#365 | D71 | semidirect |
| 152. C71 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986034 | 2 |
| C2×#17985823 | 2 |
| #22589950 | 2 |
| #22588375 | 2 |
| #22586439 | 2 |
| #22586438 | 2 |
| C2×#365×C71 | 2 |
| #12930 | 71 |