Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 628 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 |
|---|---|---|
| 2. #22594286 | C2 | semidirect |
| 3. #22587053 | C2 | semidirect |
| 4. #22586942 | C2 | semidirect |
| 5. #22586848 | C2 | semidirect |
| 6. #22586232 | C2 | semidirect |
| 7. C71×#3234 | C2 | semidirect |
| 190. #3234 | D71 | semidirect |
| 197. C71 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598793 | 2 |
| #22594286 | 2 |
| #22587053 | 2 |
| #22586942 | 2 |
| #22586848 | 2 |
| #22586232 | 2 |
| C71×#3234 | 2 |
| #10089 | 71 |