Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×#17985834 | C2 | semidirect |
| 2. C22×C71⋊C32 | C2 | semidirect |
| 3. #22590426 | C2 | semidirect |
| 4. #22586539 | C2 | semidirect |
| 5. #22586518 | C2 | semidirect |
| 6. #22586517 | C2 | semidirect |
| 7. C71×#2215 | C2 | semidirect |
| 28. C71⋊C32 | D4 | semidirect |
| 83. C22×C71 | D32 | semidirect |
| 103. #2215 | D71 | semidirect |
| 107. C71 | #13694 | semidirect |
| 186. C22 | #17985834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985834 | 2 |
| C22×C71⋊C32 | 2 |
| #22590426 | 2 |
| #22586539 | 2 |
| #22586518 | 2 |
| #22586517 | 2 |
| C71×#2215 | 2 |
| #13694 | 71 |