Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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×#17985792 | C2 | semidirect |
| 2. #22586505 | C2 | semidirect |
| 3. #22586503 | C2 | semidirect |
| 9. #532×C71 | C4 | semidirect |
| 12. #493×C71 | C4 | semidirect |
| 14. #492×C71 | C4 | semidirect |
| 16. C4×M16×C71 | C4 | semidirect |
| 30. C4⋊Q8×C71 | C2×C4 | semidirect |
| 33. #127×C71 | C2×C4 | semidirect |
| 41. C4×C8×C71 | C2×C4 | semidirect |
| 42. C4×C8×C71 | C2×C4 | semidirect |
| 135. C71 | #13584 | semidirect |
| 137. #532 | Dic71 | semidirect |
| 140. #493 | Dic71 | semidirect |
| 142. #492 | Dic71 | semidirect |
| 145. C4×M16 | Dic71 | semidirect |
| 158. C4⋊Q8 | C2×Dic71 | semidirect |
| 161. #127 | C2×Dic71 | semidirect |
| 172. C4×C8 | C2×Dic71 | semidirect |
| 173. C4×C8 | C2×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985792 | 2 |
| #22586505 | 2 |
| #22586503 | 2 |
| C71×#3151 | 2 |
| #13584 | 71 |