Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
298 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 83 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×C32×D71 | C2 | semidirect |
| 3. #22590121 | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 5. #22586519 | C2 | semidirect |
| 6. #22586517 | C2 | semidirect |
| 7. C71×#1416 | C2 | semidirect |
| 10. #17986432 | C4 | semidirect |
| 108. #1416 | D71 | semidirect |
| 111. C71 | #13615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986432 | 2 |
| C2×C32×D71 | 2 |
| #22590121 | 2 |
| #22586521 | 2 |
| #22586519 | 2 |
| #22586517 | 2 |
| C71×#1416 | 2 |
| #13615 | 71 |