Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22597057 | C2 | semidirect |
| 3. #22589163 | C2 | semidirect |
| 4. #22587009 | C2 | semidirect |
| 5. #22586899 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 11. #17986376 | C4 | semidirect |
| 12. #17986346 | C4 | semidirect |
| 99. C2×C71⋊C8 | D8 | semidirect |
| 201. #1286 | D71 | semidirect |
| 203. C71 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22597057 | 2 |
| #22589163 | 2 |
| #22587009 | 2 |
| #22586899 | 2 |
| #22586170 | 2 |
| C71×#1286 | 2 |
| #9293 | 71 |