Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #22588557 | C2 | semidirect |
| 4. #22586466 | C2 | semidirect |
| 19. #355×C71 | C4 | semidirect |
| 47. #101×C71 | C2×C4 | semidirect |
| 145. C71 | #12972 | semidirect |
| 157. #355 | Dic71 | semidirect |
| 183. #101 | C2×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591452 | 2 |
| #22588744 | 2 |
| #22588557 | 2 |
| #22586466 | 2 |
| C2×#355×C71 | 2 |
| #12972 | 71 |