Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #22597472 | C2 | semidirect |
| 2. #22587075 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22587002 | C2 | semidirect |
| 8. #17986052 | C22 | semidirect |
| 9. #17986023 | C22 | semidirect |
| 10. #17985748 | C22 | semidirect |
| 11. #17985748 | C22 | semidirect |
| 12. #17985743 | C22 | semidirect |
| 13. #17985743 | C22 | semidirect |
| 122. C71 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597472 | 2 |
| #22587075 | 2 |
| #22587008 | 2 |
| #22587002 | 2 |
| C71×#3498 | 2 |
| #17782 | 71 |