Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 4. #22586813 | C2 | semidirect |
| 5. #22586201 | C2 | semidirect |
| 6. #22586171 | C2 | semidirect |
| 7. C71×#1531 | C2 | semidirect |
| 170. #1531 | D71 | semidirect |
| 175. C71 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599292 | 2 |
| #22597418 | 2 |
| #22586950 | 2 |
| #22586813 | 2 |
| #22586201 | 2 |
| #22586171 | 2 |
| C71×#1531 | 2 |
| #9285 | 71 |