Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
676 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×Q8⋊(C71⋊C8) | C2 | semidirect |
| 4. #22586223 | C2 | semidirect |
| 5. C71×#2582 | C2 | semidirect |
| 72. C2×Q8×C71 | SD16 | semidirect |
| 154. #2582 | D71 | semidirect |
| 158. C71 | #10230 | semidirect |
| 208. C2×Q8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986199 | 2 |
| #22589145 | 2 |
| C2×Q8⋊(C71⋊C8) | 2 |
| #22586223 | 2 |
| C71×#2582 | 2 |
| #10230 | 71 |