Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#17986037 | C2 | semidirect |
| 2. C2×#17985809 | C2 | semidirect |
| 3. #22589951 | C2 | semidirect |
| 4. #22586445 | C2 | semidirect |
| 16. #467×C71 | C4 | semidirect |
| 17. #466×C71 | C4 | semidirect |
| 31. #14556060 | D4 | semidirect |
| 163. C71 | #13002 | semidirect |
| 169. #467 | Dic71 | semidirect |
| 170. #466 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986037 | 2 |
| C2×#17985809 | 2 |
| #22589951 | 2 |
| #22586445 | 2 |
| C71×#3050 | 2 |
| #13002 | 71 |