Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1056 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22599468 | C2 | semidirect |
| 3. #22587483 | C2 | semidirect |
| 4. #22587454 | C2 | semidirect |
| 5. #22587002 | C2 | semidirect |
| 6. #22586758 | C2 | semidirect |
| 7. C71×#3152 | C2 | semidirect |
| 19. #17986286 | C22 | semidirect |
| 20. #17986052 | C22 | semidirect |
| 21. #17985748 | C22 | semidirect |
| 23. #17985728 | C22 | semidirect |
| 26. C2×C4⋊Q8×C71 | C22 | semidirect |
| 28. #494×C71 | C22 | semidirect |
| 30. C4×M16×C71 | C22 | semidirect |
| 174. #3152 | D71 | semidirect |
| 179. C71 | #18715 | semidirect |
| 190. C2×C4⋊Q8 | C2×D71 | semidirect |
| 193. #494 | C2×D71 | semidirect |
| 199. C4×M16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22599468 | 2 |
| #22587483 | 2 |
| #22587454 | 2 |
| #22587002 | 2 |
| #22586758 | 2 |
| C71×#3152 | 2 |
| #18715 | 71 |