Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#17985824 | C2 | semidirect |
| 3. C2×#17985805 | C2 | semidirect |
| 4. #22590050 | C2 | semidirect |
| 5. C2×#17985783 | C2 | semidirect |
| 6. #22586450 | C2 | semidirect |
| 7. C71×#1816 | C2 | semidirect |
| 46. C2×C71⋊C16 | D4 | semidirect |
| 189. #1816 | D71 | semidirect |
| 191. C71 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598010 | 2 |
| C2×#17985824 | 2 |
| C2×#17985805 | 2 |
| #22590050 | 2 |
| C2×#17985783 | 2 |
| #22586450 | 2 |
| C71×#1816 | 2 |
| #13384 | 71 |