Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22591445 | C2 | semidirect |
| 3. #22586966 | C2 | semidirect |
| 6. #22586234 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 10. #17986368 | C4 | semidirect |
| 11. #17986364 | C4 | semidirect |
| 196. #1300 | D71 | semidirect |
| 197. C71 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598741 | 2 |
| #22591445 | 2 |
| #22586966 | 2 |
| #22586849 | 2 |
| #22586847 | 2 |
| #22586234 | 2 |
| C71×#1300 | 2 |
| #9442 | 71 |