Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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×#17985836 | C2 | semidirect |
| 2. C2×#17985834 | C2 | semidirect |
| 3. #22590426 | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 5. #22586518 | C2 | semidirect |
| 6. C22⋊(C71⋊C32) | C2 | semidirect |
| 7. C2×#508×C71 | C2 | semidirect |
| 39. Q32×C71 | D4 | semidirect |
| 42. D16×C71 | D4 | semidirect |
| 115. C2×#508 | D71 | semidirect |
| 122. C71 | #13663 | semidirect |
| 148. Q32 | C22⋊D71 | semidirect |
| 153. D16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985836 | 2 |
| C2×#17985834 | 2 |
| #22590426 | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C2×#508×C71 | 2 |
| #13663 | 71 |