Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22587088 | C2 | semidirect |
| 3. #22586302 | C2 | semidirect |
| 4. C71×#2162 | C2 | semidirect |
| 120. #2162 | D71 | semidirect |
| 123. C71 | #11649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| #22587088 | 2 |
| #22586302 | 2 |
| C71×#2162 | 2 |
| #11649 | 71 |