Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
296 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22588513 | C2 | semidirect |
| 4. #22586453 | C2 | semidirect |
| 5. #22586452 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 145. C71 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590089 | 2 |
| #22589234 | 2 |
| #22588513 | 2 |
| #22586453 | 2 |
| #22586452 | 2 |
| #22586419 | 2 |
| C71×#2148 | 2 |
| #13486 | 71 |