Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
380 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22587108 | C2 | semidirect |
| 4. #22587071 | C2 | semidirect |
| 6. #22586934 | C2 | semidirect |
| 7. C71×#1291 | C2 | semidirect |
| 187. #1291 | D71 | semidirect |
| 188. C71 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599345 | 2 |
| #22589189 | 2 |
| #22587108 | 2 |
| #22587071 | 2 |
| #22586939 | 2 |
| #22586934 | 2 |
| C71×#1291 | 2 |
| #10498 | 71 |