Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22586447 | C2 | semidirect |
| 9. #17986037 | C4 | semidirect |
| 11. C2×#14556062 | C4 | semidirect |
| 12. C2×#14556062 | C4 | semidirect |
| 142. C71 | #12870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986037 | 2 |
| #22589951 | 2 |
| #22586447 | 2 |
| C71×#1807 | 2 |
| #12870 | 71 |