Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
572 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 2. C22×#14556060 | C2 | semidirect |
| 3. C2×#17985810 | C2 | semidirect |
| 4. #22586446 | C2 | semidirect |
| 5. C71×#2112 | C2 | semidirect |
| 9. #17986240 | C4 | semidirect |
| 10. #17986235 | C4 | semidirect |
| 25. C2×Dic284 | C2×C4 | semidirect |
| 27. C2×D568 | C2×C4 | semidirect |
| 38. #14556062 | C2×C4 | semidirect |
| 42. #14556060 | D4 | semidirect |
| 139. C22×C71 | #360 | semidirect |
| 163. #2112 | D71 | semidirect |
| 165. C71 | #13001 | semidirect |
| 301. C22 | #17985810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| C22×#14556060 | 2 |
| C2×#17985810 | 2 |
| #22586446 | 2 |
| C71×#2112 | 2 |
| #13001 | 71 |