Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 75 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×#17985739 | C2 | semidirect |
| 3. #22586487 | C2 | direct (N × H) |
| 4. C2×#355×C71 | C2 | semidirect |
| 15. #17985739 | C22 | semidirect |
| 19. #355×C71 | C22 | semidirect |
| 176. C2×C71 | #1403 | semidirect |
| 180. C2×#355 | D71 | semidirect |
| 183. C71 | C2×#1403 | semidirect |
| 196. #355 | C2×D71 | semidirect |
| 355. C2 | #22586487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986176 | 2 |
| C2×#17985739 | 2 |
| #22586487 | 2 |
| C2×#355×C71 | 2 |
| C2×#1403 | 71 |