Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
598 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 598 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 |
|---|---|---|
| 2. C2×#17985801 | C2 | semidirect |
| 3. C4×#14556062 | C2 | semidirect |
| 4. C2×C4⋊C16×C71 | C2 | semidirect |
| 9. #17986376 | C4 | semidirect |
| 31. #14556062 | D4 | semidirect |
| 108. C4×C71 | #357 | semidirect |
| 121. C2×C4⋊C16 | D71 | semidirect |
| 124. C71 | #13252 | semidirect |
| 229. C4 | #17985801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986376 | 2 |
| C2×#17985801 | 2 |
| C4×#14556062 | 2 |
| C2×C4⋊C16×C71 | 2 |
| #13252 | 71 |