Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #22598056 | C2 | semidirect |
| 2. C2×#17986266 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. #22590068 | C2 | semidirect |
| 5. #22589960 | C2 | semidirect |
| 6. #22586452 | C2 | semidirect |
| 7. C2×#509×C71 | C2 | semidirect |
| 210. C2×#509 | D71 | semidirect |
| 217. C71 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598056 | 2 |
| C2×#17986266 | 2 |
| C2×#17985812 | 2 |
| #22590068 | 2 |
| #22589960 | 2 |
| #22586452 | 2 |
| C2×#509×C71 | 2 |
| #13323 | 71 |