Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 3. #22586541 | C2 | semidirect |
| 4. #22586539 | C2 | semidirect |
| 7. #17985833 | C4 | semidirect |
| 19. C71⋊C32 | C2×C4 | semidirect |
| 76. C71 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985833 | 2 |
| C2×#17985825 | 2 |
| #22586541 | 2 |
| #22586539 | 2 |
| C71×#2158 | 2 |
| #13634 | 71 |