Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 3. #22588464 | C2 | semidirect |
| 4. #22586454 | C2 | semidirect |
| 5. #22586453 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 136. C71 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985812 | 2 |
| #22590056 | 2 |
| #22588464 | 2 |
| #22586454 | 2 |
| #22586453 | 2 |
| #22586426 | 2 |
| C71×#1978 | 2 |
| #13490 | 71 |