Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
450 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 159 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. C4×#14556064 | C2 | semidirect |
| 4. #22586436 | C2 | semidirect |
| 5. C2×C4×C16×C71 | C2 | semidirect |
| 15. #17985807 | C4 | direct (N × H) |
| 34. #14556064 | C2×C4 | semidirect |
| 46. C2×C16×C71 | C2×C4 | semidirect |
| 111. C4×C71 | #359 | semidirect |
| 124. C2×C4×C16 | D71 | semidirect |
| 127. C71 | C4×#359 | semidirect |
| 160. C2×C16 | C4×D71 | semidirect |
| 235. C4 | #17985807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556150 | 2 |
| C2×#17985807 | 2 |
| C4×#14556064 | 2 |
| #22586436 | 2 |
| C2×C4×C16×C71 | 2 |
| C4×#359 | 71 |