Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590579 | C2 | semidirect |
| 3. #22587850 | C2 | semidirect |
| 4. #22586384 | C2 | semidirect |
| 5. #22586307 | C2 | semidirect |
| 6. #22586297 | C2 | semidirect |
| 7. C71×#2226 | C2 | semidirect |
| 19. #17985775 | C22 | semidirect |
| 20. #17985750 | C22 | semidirect |
| 22. #500×C71 | C22 | semidirect |
| 25. C4⋊C16×C71 | C22 | semidirect |
| 98. D8×C71 | SD16 | semidirect |
| 169. #2226 | D71 | semidirect |
| 174. C71 | #12378 | semidirect |
| 177. #500 | C2×D71 | semidirect |
| 187. C4⋊C16 | C2×D71 | semidirect |
| 253. D8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599950 | 2 |
| #22590579 | 2 |
| #22587850 | 2 |
| #22586384 | 2 |
| #22586307 | 2 |
| #22586297 | 2 |
| C71×#2226 | 2 |
| #12378 | 71 |