Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 12. #17986401 | C4 | semidirect |
| 13. #17986397 | C4 | semidirect |
| 33. #14556068 | Q8 | semidirect |
| 35. C2×C71⋊C16 | Q8 | semidirect |
| 131. C71 | #13291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598871 | 2 |
| #22589945 | 2 |
| #22586454 | 2 |
| #22586445 | 2 |
| #22586441 | 2 |
| #22586440 | 2 |
| C71×#1833 | 2 |
| #13291 | 71 |