Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 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. #22599723 | C2 | semidirect |
| 3. #22587565 | C2 | semidirect |
| 4. #22587516 | C2 | semidirect |
| 5. #22587075 | C2 | semidirect |
| 6. #22586792 | C2 | semidirect |
| 7. C71×#3131 | C2 | semidirect |
| 17. #17986276 | C22 | semidirect |
| 19. #17986201 | C22 | semidirect |
| 21. #17986023 | C22 | semidirect |
| 22. #17985748 | C22 | semidirect |
| 24. #17985728 | C22 | semidirect |
| 25. #533×C71 | C22 | semidirect |
| 28. #487×C71 | C22 | semidirect |
| 31. C2×C4×C8×C71 | C22 | semidirect |
| 182. #3131 | D71 | semidirect |
| 187. C71 | #18691 | semidirect |
| 195. #533 | C2×D71 | semidirect |
| 199. #487 | C2×D71 | semidirect |
| 208. C2×C4×C8 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22599723 | 2 |
| #22587565 | 2 |
| #22587516 | 2 |
| #22587075 | 2 |
| #22586792 | 2 |
| C71×#3131 | 2 |
| #18691 | 71 |