Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22597281 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1518 | C2 | semidirect |
| 9. #17986373 | C4 | semidirect |
| 10. #17986347 | C4 | semidirect |
| 89. C2×C71⋊C8 | SD16 | semidirect |
| 181. #1518 | D71 | semidirect |
| 184. C71 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22597281 | 2 |
| #22589163 | 2 |
| #22587007 | 2 |
| #22586198 | 2 |
| #22586170 | 2 |
| C71×#1518 | 2 |
| #9294 | 71 |