Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 2. C2×#17985833 | C2 | semidirect |
| 3. #22586526 | C2 | direct (N × H) |
| 4. C2×#367×C71 | C2 | semidirect |
| 8. #17986431 | C4 | semidirect |
| 10. C2×Dic568 | C4 | semidirect |
| 12. C2×D1136 | C4 | semidirect |
| 14. #17985833 | C22 | semidirect |
| 19. #367×C71 | C22 | semidirect |
| 29. Dic568 | C2×C4 | semidirect |
| 33. D1136 | C2×C4 | semidirect |
| 111. C2×C71 | #1418 | semidirect |
| 116. C2×#367 | D71 | semidirect |
| 118. C71 | C2×#1418 | semidirect |
| 133. #367 | C2×D71 | semidirect |
| 225. C2 | #22586526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986431 | 2 |
| C2×#17985833 | 2 |
| #22586526 | 2 |
| C2×#367×C71 | 2 |
| C2×#1418 | 71 |