Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22589945 | C2 | semidirect |
| 5. #22586454 | C2 | semidirect |
| 6. #22586447 | C2 | semidirect |
| 7. C71×#1951 | C2 | semidirect |
| 14. #17985814 | C4 | semidirect |
| 15. #17985811 | C4 | semidirect |
| 144. #1951 | D71 | semidirect |
| 147. C71 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590087 | 2 |
| C2×#17985808 | 2 |
| #22589945 | 2 |
| #22589238 | 2 |
| #22586454 | 2 |
| #22586447 | 2 |
| C71×#1951 | 2 |
| #13156 | 71 |