Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22597191 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22589251 | C2 | semidirect |
| 5. #22586435 | C2 | semidirect |
| 6. #22586430 | C2 | semidirect |
| 7. C71×#2140 | C2 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 42. C2×C71⋊C16 | C2×C4 | semidirect |
| 56. C2×D8×C71 | C2×C4 | semidirect |
| 169. #2140 | D71 | semidirect |
| 173. C71 | #13017 | semidirect |
| 205. C2×D8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| #22597191 | 2 |
| C2×#17985813 | 2 |
| #22589251 | 2 |
| #22586435 | 2 |
| #22586430 | 2 |
| C71×#2140 | 2 |
| #13017 | 71 |