Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
888 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22589168 | C2 | semidirect |
| 3. #22587075 | C2 | semidirect |
| 4. #22587073 | C2 | semidirect |
| 5. C71×#1962 | C2 | semidirect |
| 6. #17986741 | C4 | semidirect |
| 14. #17986023 | C22 | semidirect |
| 21. #423×C71 | C22 | semidirect |
| 23. C43×C71 | C22 | semidirect |
| 169. #1962 | D71 | semidirect |
| 172. C71 | #8530 | semidirect |
| 183. #423 | C2×D71 | semidirect |
| 186. C43 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22589168 | 2 |
| #22587075 | 2 |
| #22587073 | 2 |
| C71×#1962 | 2 |
| #8530 | 71 |